If I lose/fail a raid at an EX Eligible gym, do I still get the lottery ticket?

I believe you need to at least defeat the boss, but actually catching it is optional.

No, you need to defeat the boss. You don't have to catch it though.

If you see/hear about an egg at an EX gym, just go and wait til hatch. You say it is an active Pokémon area and the majority use multiphones. A decent chance the boss can be beat. Even if nobody is there type on whatever communication system your area has: tier 3/4 raid at EX gym. I’ve gotten people to rush to do a Nidoking.

You have to win.