You need to find the journal page with a certain recipe to get a Lilith. The specific page is number 11. You need to use the cauldron to craft and use the suppressant before you can pick up a Lilith. True Sight might be randomized but making it rain and finding out how to turn it to night will let you find those 3 mushrooms with 100% certainty. I could tell you my recipe for True Sight but it might not work. I could also tell you the formula for the suppressant but I don't think you can craft it without physically reading Journal Entry 11.
I just tried it on a new save and it is in fact the same combination. Unless I got extremely lucky the order remained the same. The appearance of the mushrooms change on each new game. You need to eat an Echoshroom, a MindSap, and a Deathcandle in that order. However, if you eat a Dreamshroom you need to start over. Without being able to summon the rain you would have to either guess if the mushroom you cannot identify is a MindSap or a Dreamshroom. Unless you use the guidebook to identify the unknown mushroom to see if it is a MindSap or Dreamshroom.