2 Legendary Skins, 1 Epic Skin and NO Summoner Icon

Ultimates always do, and Legendary/Epic skins more often than not come with their own Summoner Icons that you can get either through an event or by buying the icon itself.

For my case, I need to clarify that the icons I'm bringing up specifically let you chose and image of an actual champion not just something related to the champion.

Let's review them real quick: https://vignette2.wikia.nocookie.net/leagueoflegends/images/3/38/ProfileIcon0948_Burning_Hunger.png/revision/latest/scale-to-width-down/64?cb=20170517185119 https://vignette3.wikia.nocookie.net/leagueoflegends/images/3/3f/ProfileIcon0949_Drop_Dead.png/revision/latest/scale-to-width-down/64?cb=20170517185047 https://vignette2.wikia.nocookie.net/leagueoflegends/images/0/01/ProfileIcon1391_Little_Devil_Teemo.png/revision/latest/scale-to-width-down/64?cb=20170505004408 https://vignette2.wikia.nocookie.net/leagueoflegends/images/9/99/ProfileIcon1113_Draven_Draven_Icon_Icon.png/revision/latest/scale-to-width-down/64?cb=20170504221749 https://vignette4.wikia.nocookie.net/leagueoflegends/images/7/73/ProfileIcon1456_Heartseeker_Lucian.png/revision/latest/scale-to-width-down/64?cb=20170505005837 https://vignette1.wikia.nocookie.net/leagueoflegends/images/e/e8/ProfileIcon1455_Heartseeker_Quinn.png/revision/latest/scale-to-width-down/64?cb=20170504194324 https://vignette3.wikia.nocookie.net/leagueoflegends/images/9/9e/ProfileIcon1636_Cosmic_Reaver.png/revision/latest/scale-to-width-down/64?cb=20170505021239 https://vignette4.wikia.nocookie.net/leagueoflegends/images/d/d6/ProfileIcon1596_Dragon_Sorceress.png/revision/latest/scale-to-width-down/64?cb=20170505012815 https://vignette3.wikia.nocookie.net/leagueoflegends/images/1/1c/ProfileIcon1595_Dragonslayer_Xin_Zhao.png/revision/latest/scale-to-width-down/64?cb=20170505004231 https://vignette3.wikia.nocookie.net/leagueoflegends/images/1/1c/ProfileIcon1381_Mark_of_the_Star_Guardian.png/revision/latest/scale-to-width-down/64?cb=20170504235729 https://vignette2.wikia.nocookie.net/leagueoflegends/images/f/f0/ProfileIcon1641_Dark_Star_Kha%27Zix.png/revision/latest/scale-to-width-down/64?cb=20170505020751 https://vignette3.wikia.nocookie.net/leagueoflegends/images/7/7d/ProfileIcon1640_Dark_Star_Orianna.png/revision/latest/scale-to-width-down/64?cb=20170505013220 https://vignette4.wikia.nocookie.net/leagueoflegends/images/1/1e/ProfileIcon1162_El_Rayo.png/revision/latest/scale-to-width-down/64?cb=20170505000033 https://vignette1.wikia.nocookie.net/leagueoflegends/images/1/1f/ProfileIcon1161_El_Macho.png/revision/latest/scale-to-width-down/64?cb=20170504223921 https://vignette2.wikia.nocookie.net/leagueoflegends/images/2/2e/ProfileIcon1160_El_Le%C3%B3n.png/revision/latest/scale-to-width-down/64?cb=20170504230233 https://vignette4.wikia.nocookie.net/leagueoflegends/images/0/03/ProfileIcon1159_El_Tigre.png/revision/latest/scale-to-width-down/64?cb=20170505004447 https://vignette2.wikia.nocookie.net/leagueoflegends/images/6/6d/ProfileIcon1157_Super_Galaxy_Shyvana.png/revision/latest/scale-to-width-down/64?cb=20170504235649 https://vignette2.wikia.nocookie.net/leagueoflegends/images/5/51/ProfileIcon1156_Super_Galaxy_Wolf.png/revision/latest/scale-to-width-down/64?cb=20170505003837 https://vignette2.wikia.nocookie.net/leagueoflegends/images/2/24/ProfileIcon1155_Super_Galaxy_Lamb.png/revision/latest/scale-to-width-down/64?cb=20170505010052 https://vignette1.wikia.nocookie.net/leagueoflegends/images/3/39/ProfileIcon1153_Super_Galaxy_Fizz.png/revision/latest/scale-to-width-down/64?cb=20170505021840 https://vignette2.wikia.nocookie.net/leagueoflegends/images/c/c6/ProfileIcon0914_PROJECT_Lucian.png/revision/latest/scale-to-width-down/64?cb=20170504232434 https://vignette3.wikia.nocookie.net/leagueoflegends/images/2/21/ProfileIcon0913_PROJECT_Fiora.png/revision/latest/scale-to-width-down/64?cb=20170504223730 https://vignette4.wikia.nocookie.net/leagueoflegends/images/3/35/ProfileIcon0912_PROJECT_Leona.png/revision/latest/scale-to-width-down/64?cb=20170504222824 https://vignette1.wikia.nocookie.net/leagueoflegends/images/e/e8/ProfileIcon0911_PROJECT_Zed.png/revision/latest/scale-to-width-down/64?cb=20170504223747 https://vignette1.wikia.nocookie.net/leagueoflegends/images/b/b8/ProfileIcon0910_PROJECT_Yi.png/revision/latest/scale-to-width-down/64?cb=20170504232413 https://vignette4.wikia.nocookie.net/leagueoflegends/images/c/c5/ProfileIcon1231_PROJECT_Katarina.png/revision/latest/scale-to-width-down/64?cb=20170505005706 https://vignette1.wikia.nocookie.net/leagueoflegends/images/6/66/ProfileIcon1228_PROJECT_Ekko.png/revision/latest/scale-to-width-down/64?cb=20170505021801 https://vignette3.wikia.nocookie.net/leagueoflegends/images/a/a5/ProfileIcon1227_PROJECT_Ashe.png/revision/latest/scale-to-width-down/64?cb=20170505012545 https://vignette2.wikia.nocookie.net/leagueoflegends/images/7/73/ProfileIcon1225_Recon_PROJECT_Ashe.png/revision/latest/scale-to-width-down/64?cb=20170505012528 https://vignette1.wikia.nocookie.net/leagueoflegends/images/5/56/ProfileIcon0870_Pool_Party_Zac.png/revision/latest/scale-to-width-down/64?cb=20170517185742 https://vignette4.wikia.nocookie.net/leagueoflegends/images/8/83/ProfileIcon0750_Blood_Moon.png/revision/latest/scale-to-width-down/64?cb=20170215232823 https://vignette4.wikia.nocookie.net/leagueoflegends/images/2/2f/ProfileIcon1108_Blood_Moon_Yasuo.png/revision/latest/scale-to-width-down/64?cb=20170504230101 https://vignette2.wikia.nocookie.net/leagueoflegends/images/f/f3/ProfileIcon1107_Blood_Moon_Kennen.png/revision/latest/scale-to-width-down/64?cb=20170505000123 https://vignette2.wikia.nocookie.net/leagueoflegends/images/f/f8/ProfileIcon1591_Blood_Moon_Talon.png/revision/latest/scale-to-width-down/64?cb=20170505004256 https://vignette2.wikia.nocookie.net/leagueoflegends/images/2/23/ProfileIcon1590_Blood_Moon_Twisted_Fate.png/revision/latest/scale-to-width-down/64?cb=20170505005916 https://vignette3.wikia.nocookie.net/leagueoflegends/images/6/6c/ProfileIcon1589_Blood_Moon_Diana.png/revision/latest/scale-to-width-down/64?cb=20170504192206 https://vignette1.wikia.nocookie.net/leagueoflegends/images/7/7b/ProfileIcon1588_Blood_Moon_Jhin.png/revision/latest/scale-to-width-down/64?cb=20170505000056 https://vignette1.wikia.nocookie.net/leagueoflegends/images/5/52/ProfileIcon1297_Arcade_Ezreal.png/revision/latest/scale-to-width-down/64?cb=20170505013608 https://vignette1.wikia.nocookie.net/leagueoflegends/images/e/e2/ProfileIcon1296_Arcade_Ahri.png/revision/latest/scale-to-width-down/64?cb=20170505012632 https://vignette1.wikia.nocookie.net/leagueoflegends/images/7/78/ProfileIcon1295_Arcade_Corki.png/revision/latest/scale-to-width-down/64?cb=20170505020346 https://vignette2.wikia.nocookie.net/leagueoflegends/images/b/bb/ProfileIcon1134_Mecha_Zero.png/revision/latest/scale-to-width-down/64?cb=20170505000016 https://vignette3.wikia.nocookie.net/leagueoflegends/images/3/3c/ProfileIcon0787_Omega_Squad_Teemo.png/revision/latest/scale-to-width-down/64?cb=20170504213211 https://vignette3.wikia.nocookie.net/leagueoflegends/images/4/47/ProfileIcon1629_Immortal_Sight.png/revision/latest/scale-to-width-down/64?cb=20170505020638 https://vignette1.wikia.nocookie.net/leagueoflegends/images/4/49/ProfileIcon1644_Pulsefire_Ezreal.png/revision/latest/scale-to-width-down/64?cb=20170505155524 https://vignette1.wikia.nocookie.net/leagueoflegends/images/0/06/ProfileIcon1643_Pulsefire_Caitlyn.png/revision/latest/scale-to-width-down/64?cb=20170505155504 https://vignette4.wikia.nocookie.net/leagueoflegends/images/d/da/ProfileIcon1116_Urf_Kench.png/revision/latest/scale-to-width-down/64?cb=20170504230216 https://vignette4.wikia.nocookie.net/leagueoflegends/images/6/6f/ProfileIcon1115_Definitely_Not_a_Vel%27Koz_Icon.png/revision/latest/scale-to-width-down/64?cb=20170504223443 https://vignette2.wikia.nocookie.net/leagueoflegends/images/f/f8/ProfileIcon1632_Conqueror_Karma.png/revision/latest/scale-to-width-down/64?cb=20170505004020

Some champions have more than one icon, and some even got an icon with no skin attached to them:

https://vignette3.wikia.nocookie.net/leagueoflegends/images/c/c6/ProfileIcon0939_Kindred_Lamb.png/revision/latest/scale-to-width-down/64?cb=20170517185414 https://vignette1.wikia.nocookie.net/leagueoflegends/images/9/97/ProfileIcon0938_Kindred_Wolf.png/revision/latest/scale-to-width-down/64?cb=20170517185434 https://vignette4.wikia.nocookie.net/leagueoflegends/images/f/f0/ProfileIcon1633_Gift_of_Magic.png/revision/latest/scale-to-width-down/64?cb=20170505024832 https://vignette1.wikia.nocookie.net/leagueoflegends/images/a/a5/ProfileIcon1111_Draaaaven.png/revision/latest/scale-to-width-down/64?cb=20170505003818 https://vignette1.wikia.nocookie.net/leagueoflegends/images/d/df/ProfileIcon1112_Draven_Winion.png/revision/latest/scale-to-width-down/64?cb=20170504235629 https://vignette3.wikia.nocookie.net/leagueoflegends/images/b/b7/ProfileIcon0902_Act_3_Lessons_in_Power.png/revision/latest/scale-to-width-down/64?cb=20170504235401 https://vignette1.wikia.nocookie.net/leagueoflegends/images/f/f8/ProfileIcon0901_Act_3_Setting_Things_Right.png/revision/latest/scale-to-width-down/64?cb=20170504235340 https://vignette1.wikia.nocookie.net/leagueoflegends/images/6/6b/ProfileIcon0900_Act_2_Above_the_Abyss.png/revision/latest/scale-to-width-down/64?cb=20170504235323 https://vignette3.wikia.nocookie.net/leagueoflegends/images/8/84/ProfileIcon0899_Act_2_Taking_a_Dive.png/revision/latest/scale-to-width-down/64?cb=20170504235303 https://vignette1.wikia.nocookie.net/leagueoflegends/images/b/b2/ProfileIcon0898_Act_1_The_Job.png/revision/latest/scale-to-width-down/64?cb=20170504235244 https://vignette3.wikia.nocookie.net/leagueoflegends/images/1/17/ProfileIcon0897_Act_1_Reunion.png/revision/latest/scale-to-width-down/64?cb=20170504235223 https://vignette2.wikia.nocookie.net/leagueoflegends/images/9/90/ProfileIcon0781_Nemesis_Draft.png/revision/latest/scale-to-width-down/64?cb=20170504221513 https://vignette3.wikia.nocookie.net/leagueoflegends/images/8/81/ProfileIcon0673_Doom.png/revision/latest/scale-to-width-down/64?cb=20170504215259 https://vignette1.wikia.nocookie.net/leagueoflegends/images/2/22/ProfileIcon0664_Mirror_Mode.png/revision/latest/scale-to-width-down/64?cb=20170517181936 https://vignette3.wikia.nocookie.net/leagueoflegends/images/7/76/ProfileIcon1630_Astronaut_Teemo.png/revision/latest/scale-to-width-down/64?cb=20170505021325 https://vignette1.wikia.nocookie.net/leagueoflegends/images/7/74/ProfileIcon0773_Fizz.png/revision/latest/scale-to-width-down/64?cb=20170504215037 https://vignette1.wikia.nocookie.net/leagueoflegends/images/3/33/ProfileIcon1587_Koi_Nami.png/revision/latest/scale-to-width-down/64?cb=20170505010201

So that's all nice and fun, and I may have missed a couple. Then there's one champion that has 2 legendary skins and one epic skin. A firefighter, a dragon trainer and a witch. And as it turns out she has...

Zero Summoner icons

Must I give up on this quest?