Lita's +1 damage bonus only applies to Fight actions, not to any other effects that deal damage (Sneak Attack, etc.).
When you 'take control' of a card, it enters your play area (not your hand).
You take control of Lita only temporarily, until the end of the scenario. Taking control of her doesn't make her a part of your deck.
- If Lita leaves play while a player controls her temporarily during "The Gathering" scenario (i.e. while she is technically not a part of that player's deck), remove her from the game (do not place her into any discard pile). This does not affect possible scenario resolutions.
While you control Lita Chantler, she gains:
"Each investigator at your location gets +1 .
When an investigator at your location successfully attacks a Monster enemy: That investigator deals +1 damage."
Lita Chantler: arsonist, ghoul-slayer, and Umordhoth's favorite snack. How is it that, over three years after the release of the Arkham Horror LCG, this torch-wielding termagant still has no review? It's time to redress this wrong.
There's two ways to think about Lita -- as an interesting story asset during The Night of the Zealot (she appears to be said Zealot), and as a standard ally, if you decide to make The Night of the Zealot the first chapter of a multi-set campaign.
In the Night of the Zealot, Lita shows up in your house while you run, shrieking, from a ghoul priest. But she's skeptical that you really need any help; her preference is to watch your duel to the death from the comfort of your parlor. If, however, you engage her in conversation and make a well-organized and informed case as to why she should rescue you from the deranged beast clawing at your back, she'll do what she can. Together, you'll defrock the ghoul priest, and then arrive a crossroads. Lita wants to burn your house: if you demur, she storms off in disgust; if you let her, she'll be your BFF, but you'll never quite be the same (I'm not sure if it's the house burning, or the crazed look in Lita's eyes as it burns, but you'll collect your first mental trauma here). In the next two scenarios, Lita will be an excellent pull. Even if you're not going up against monster enemies (her flavor of choice), the multi-investigator fight bonus is wonderful, and she soaks damage and horror like a champ. In the Devourer Below, she may get you out of a sticky situation indeed.
I think the more interesting question, though, is how Lita does BEYOND Night of the Zealot, if you survive it, and if your investigator is in shape for further mythos-plumbing. In short, she does well. Possibly best-card-in-the-game well, excluding one or two permanents. With her massive soak capacity, her zero-resource play cost, and her ability to buff the whole group, not just you, I'd pay 10xp or more to put her in certain decks. And how good is the bonus against monsters? Real good. There are about 120 enemy encounter cards with the monster trait, not to mention some dozen or so weakness enemies, including the signature weaknesses of Father Mateo, Tony, Norman Withers, and William Yorick.
If you want Lita to Undo the Circle with you, or Tread the Path to Carcosa, or Eat some Dreams, just remember that you'll be starting that campaign with a minimum of three mental trauma, one from watching Lita burn your house, and two from your brush with Umordhoth. Of course, you'll have a pile of experience as well, so it might even out somewhat, especially for high-sanity investigators like Norman. Still, I can guarantee for she'll be a dream-pull in just about every scenario.