Lama Ladonna is unlocked by surviving at least 20 minutes with any other character on any stage where there is at least 10% Curse active. Once she is unlocked, you will need to purchase her for 500 gold (this does scale, so the value may not be exactly this), then she becomes playable. Also, she can be unlocked in the Forbidden Scrolls of Morbane if you have them by casting the spell 'superladonna'.
Surviving with Lama is really not that much different than surviving for that long with any of the other playable characters: concentrate on evolving the weapons you feel are most effective, as well as leveling up the starting Axe (which is evolved with the Candelabrador). Also, if you have any Curse purchased, it may be helpful to refund all your points to remove those then reallocate.
I would suggest using the Library level, as that seems to be the easiest "normal" stage in the game.