Being someone who hates cheese-loaded foods and especially vegetarian food that is loaded with cheese (lazy), I'd be happy to cook for this friend! I hardly use cheese in actual dishes. I usually just snack on cheese by itself when I have it.
Indian, Indonesian, Chinese, Japanese, and Korean have plenty of vegetarian dishes and they're completely cheese-free.
Mexican can also be made vegetarian pretty easily and while there's some cheese involved in things like tostadas, it's minimal and can be easily left off. Most tacos don't involve any cheese either.
Neither does a good tortilla soup. It can be made completely vegetarian and the chilies (no chili powder, please, must be dried whole chilies) used give it plenty of flavor, while the garnishes (avocado, cabbage, some limes, radishes, sour cream, and of course, fried tortilla strips, among others) make it really visually and texturally appealing.
Dishes just off the top of my head that can be made this time of year that are completely vegetarian.
Succotash (no bacon needed to make this delicious), fresh creamed corn, stuffed summer squash, various frittatas (I made a scallion one recently that was awesome; I almost never put cheese in frittata), tortilla espaņola, shakshuka, various soups, vegetable fried rice, artichoke tart, vegetable patties, fritters, savory custards, great vegetarian chili. There's a lot more, but I'm going to stop because I can think of way more things to cook that contain no cheese than ones that do.
I rep it a lot, but you should really check out Herbivoracious if you want more concrete ideas. For one thing, he breaks it down how to cook delicious tofu, and puts to rest myths like marinating doing a damn thing.
Ottolenghi's books and column are also a good source (he's not vegetarian, and does use cheese in a lot of vegetarian dishes, but he also does plenty without and he's really imaginative):