I think the only reason some people want Lana to still be alive is that she'd be another girl to possibly fuck.
There's no reason for Jill to lie, I think the copium used is that Jill's parents told her that Lana died when she didn't. I'm pretty sure Jill would have wanted to visit her grave at some point though so that theory would fall down.
Jill's campaign is obviously something to do with Lana, and it's likely that's going to be the "in" to get Jill involved in the drugs storyline, she's either going to be campaigning for zero tolerance on drugs, or campaigning for better support for addicts, bringing her either on a collision course with Quinn et al, or actually coming in on their side if there's an attempt to remove all students involved when the drugs become public knowledge.