The most important word of this card is "Then". If Lola has a Permanent of her role (or a card that can't be discarded like Unscrupulous Loan), she will not discard all cards of her current role, and the second part of Crisis of Identity will not happen (no card discarded from deck and no role switch).
So, if you buy a Permanent of each class, half of your investigator weakness will be nullified. As a nice side effect, you will get full bonus from the Synergy cards, all of those (except Close the Circle) beeing events or skills and therefore immune to Crisis of Identity,
For example, i like to start my campaign with In the Thick of It, Shrewd Analysis Short Supply, Charon's Obol and Arcane Research, before dealing with with Sacred Covenant on second scenario.
If Charon's Obol scares you, you can wait the second scenario for Adaptable. I would still keep ItToI'xp for some synergy cards.
Edit : thanks to the latest taboo, this review has become irrelevant :/