Almost everything I can think of has one of those three things.
What about boiled eggs with some salt sprinkled on them? Just be sure to keep them cool with an ice pack or two. Will she eat lunch meat or cut up chicken breast wrapped in a lettuce leaf? An apple and sugar snap peas, dried fruit (or does that have added sugar?). sugar free cinnimon applesauce. Blueberries. Avacado is awesome, has good fats.
Maybe check out
http://www.amazon.com/Recipes-Repair-Lyme-Disease-Cookboo...
Also google 'lyme disease diet recipes' and you will see a lot of blogs and books out there.
Can you meet with a nutritionist and together come up with a list of foods she CAN eat. Ask her to focus on replacement foods... like, instead of grains, eat sweet potatoes and potatoes as a carb. And... instead of milk, use almond or soy milk. Instead of dairy, use beans for protein. Ask for a list of specific foods and brands. Bring along containers and go over the nutritional information together so you know exactly what to look for to avoid. Ask for her to create a complete sample menu for an entire day that will get all of your daughters dietary needs met. Maybe give the nutritionist a heads up about what you are looking for before you meet with her, so she can research it a little bit and be prepared to give you valuable information.
Make this your mission, like a game. Use all resources you can, and if they don't give you what you need, call someone else and ask them. The more 'experts' you consult for help getting her through this diet, the better.
It's going to be tough for you for awhile. Good luck to you, hang in there.
ETA will any of these work? They sell them at target...
http://www.gopicnic.com/Special-Diets/Gluten-Free