I have to disagree. Liz is a drama queen. I don't believe she actually has the allergies she claims. For one thing. I don't think they'd cast someone with true anaphylaxis--too much danger of them accidently ingesting something and going into anaphylactic shock.
A couple examples: I have eczema. Red foods (red peppers, strawberries) can make it flare up and itch. I'm NOT going to die, it's just (literally) irritating. I avoid the foods, but I'm not truly allergic. Similarly, some people are actually allergic to dairy (which must suck). OTOH, 40% of adults have a lactose intolerance, which won't kill you, but WILL make you uncomfortable for a couple days. The latter isn't an allergy, but the former is, and can lead to anaphylactic shock and potentially death.
The fact that Liz claims all these allergies, woe is me, but can miraculously eat every thing on the Applebee's reward is just too over-the-top. And Q is entitled to take the people HE wants on HIS reward.