From my analysis, It looks like your deaths were over buffs (Jungle fights), or just from lane fighting the matchup.
How i would have played the build would have been: Cloth 5 Dorans Ring, Dorans Ring -> Morellos, CDR boots, Zhonyas and try for a mid game power spike where you can get fed and carry over or get the adc fed to carry the game and take objectives.
-I wouldn't bother to fight that match-up, and just wave-clear and ult myself when he ults (It's like a zhonyas) or him under tower and then CC him to death. (Or if he blew his cd's i could wear him down with Q and all in)
-One of my favorite parts about liss is her CC for ganking botlane with that strong all-in. after boots / Morrellos you'll have 40% CDR and you can ult every ~50 Seconds Which is definitely worth it over Magic penn boots. You'ed be able to go botlane and get a kill every time it's up. I tend to find that botlane carries games, and you need to camp it and kill it as much as possible.
In that particular game, a good roam about 7 mins in (Level 6) might have been able to get your adc back into the game, and gotten you some more gold. (It looks like you lost the game due to jungle presence, and your jungler had little presence, so it was up to you to gank lanes, or request to do a 4v2 and get them kills / Towers)
As lissandra, You have 2 possibilities to win team fights: All in CC and try to burst the enemy carry that's valuable or: Protect the ally ADC, by peeling. This depends on who's fed, and you should peel for your adc since he's behind instead of diving.