Enemy assassins
Honestly I still pick Lulu mid every time I see a Kat or Akali. You first back Negatron (now that chalice is quote on quote nerfed) and you first item Abyssal, you have high base damage and good lock down to mess up an assassin's combo. I've never actually lost lane against either of them as Lulu (although Lulu does dip off after mid game so if they get fed in teamfights they tend to outscale you)
Lulu can give champions like Olaf, Udyr, Volibear, Singed or Rengar the speed boost they need to catch the enemy team.
Most support champions have some sort of MS boost. On top of the champions above normally have good MS (and Rengo has a gapcloser). Normally you want it more for the second part of your 'initiation' reason. You want to pick Lulu into a composition where you have a melee champion (often a carry) who wants to position themselves in the middle of the enemies and can use the safety of the knockup. Someone like Morgana or Katarina can use the knockup to get their ults off safely and optimally. Or a bruiser like Vi who can get in the middle of the enemies by ulting in, but really lacks the ability to survive/escape after her abilities are blown, where the knockup on your ult would give her the HP and the time to take out the enemy carry and either make it out of the pit or thrive her way through the enemies as the clean up crew while she has her team backing her up. Someone who doesn't already have a good way into the enemy team doesn't particularly want Lulu on their team. Most supports have that MS boost and there are more useful tools to them.
If you have an Udyr or Singed who need initiation you want a Leona to dive in or a Nami to ult/bubble maybe even a Braum ult. If your melee carry can't wedge themselves into the enemy team without help they want somebody with better CC.
As for the second part of what I was saying, Lulu is also useful against heavy dive compositions. A Yi who Qs in can easily found himself chain CCed by a polymorph and then an ult on the carry he is focusing. When the enemy team has 2 or more champions who enjoy diving into the enemy team without a secure way back out (like LeBlanc who can instantly port back), Lulu's ult is a good way to tie the enemies down while protecting their biggest target.
In short you pick Lulu with/against teams that are good at shoving into the middle of the enemy team. A team that relies on MS (like a Sivir ult or Talisman or Sona E) to initiate is better repelled by a good Janna Q or a good Nami ult.
You know that fed teammate who is dominating? Lulu can give them speed, max health, a shield, magic damage on autoattacks, a knock-up around them along with heavy slows. She can turn any fed champion into a monster to deal with. So if I expect one of my teammates is going to carry us, Lulu is the choice to make sure that happens.
I have found Lulu very effective to 2v5 or 3v5 in, although I wouldn't pick her solely because she might find a teammate who can carry. I would definitely look to see if she's against a botlane she can do well in, and if she has teammates who can make use of the knockup on her ult even if they aren't hypercarrying, before deciding to go Lulu.
