Young Guest with Allergies to Eggs, Dairy, Peanuts and Some Soy.
Read all labels very closely, even for cold cuts. Some contain fillers that might have the allegens you're trying to avoid.
You can try tuna salad, or chicken salad if they don't eat fish. You can make homemade chicken fingers, too, for a healthy fast-foodish meal.
Go for pasta - either warm or in salads - making sure you use egg-free brands. Or make fajitas, because anything you eat with your hands must be good. :-)
I have a friend in the same situation. She ususally has her child's meal already planned out as to not burden anyone else. However, here's what I've learned because it's also always nice to be hospitable. You're friend I'm sure will appreciate the gesture.
Since it's the summer time, you can grill or bbq any meat, veggie and carb option. Indoor grills work great too. You can even oven roast. What you do need to think about how to flavor these items.
There's the traditional bbq sauces in the bottle. Most don't have soy, but do read the label carefully for soya and lechitin which are soy products. Vegetable oil is also basically soybean oil, so don't marinate in that either. In terms of salads, don't serve any with mayonnaise as that is egg and oil. Potatoes or rice are good carb options. Oven fries are great. Dipping makes kids happy. Ketchup, mustard, and bbq sauce usually don't have soy.. but do read.
Fruity popsicles are so yummy and fun for adults too as dessert options. Sorbets are good, not sherbets as they are usually milk based. Fresh fruit can be a healthy option as well. I suggest going all out and buying the organic stuff to make your friend feel special. You really are thinking about her family and their well being.
In any case, ask your friend. I'm sure she has wonderful ideas as well. My ideas are things that really the whole family can enjoy so the young guest doesn't feel left out. Can you imagine what the young one must go through in school? Good luck and you're such a great friend for even seeking help.