So as you feed Lilly she will stop eating with a wardrobe problem (this requires you to get Beth, the running girls phone number, then after building the relationship up by calling her you can ask for help, you need to get a message about asking your friends from check in on Lilly after getting the number)
Next continue feeding until Lilly has stomach problems, then Call Steph, she will mention herbal pills (bought at the Whole Foods after this) after giving these to Lilly then the second cookbook appears (it is a whole chain of flags) thankfully the final cookbook just needs Lilly to reach the last roadblock where you call Jamie (this is after the 'Sponsor' event)
Honestly out of all the characters, Lilly is the most time consuming one to do, even with the guide