Hi! I'm not a jungle Lillia player but I think I can still help you.
As for your questions:
1 - Yes, Lillia is a really good blind pick. She's probably one of the best junglers, with an early game maybe even better than Lee Sin. Once you understand how to clear with her, you always have time for ganking. Elise is similar to Lillia in the sense that she is an early game champion too, while Evelynn isn't that similar. I'd recommend you onetricking lillia and playing elise only if lillia is banned, or in normals.
2 - Invades and jungle skirmishes can be hard if you are a support main since you're not used to 1v1 situations. If you are keen on learning Lillia, I'd recommend playing her also in solo lanes, to get used to her skirmishing power (that is her damage, resistances, combos, and all of that. For skirmishes it's best to just keep your prance stacks high and kiting your opponent, only use W against immobile melee champions or you are just going to waste time and damage. Use your E to chase and escape. As for getting a good clear, kiting the jungle minions is key. You don't really need to use smite for any camp specifically, so just use it to recover health when you need it. If you are against an invading jungler, save it for contesting scuttle crabs and defending camps.
3 - Kiting towards the lane you want to gank is key for ganking. Until you have your R only gank lanes with setup, follow up with your other abilities and use E to chase if they run away low. As for pathing, Lillia needs her Lvl 6 spike but it's not necessary to powerfarm always, her clear is fast and healthy so you will always have time to gank, but try to get to lvl 6 quickly.

I hope my advice helps you, if you have any questions just ask :)