Do food allergies last a lifetime, or do they eventually go away?

Go away in kids. You are 37 years old. Although I have seen fish allergy resolve after 20 years or so, for most adults food allergies do not go away. In children & infants most dairy, egg, wheat, soy & corn allergy resolves in a few years. For example, for dairy we see at least 80% resolution in 10-15 years. Even peanut & tree nut allergy resolves spontaneously in 20-25% of kids.
No. The immune system builds more memory of prior exposure over time, so the likelihood of food allergies decreasing or resolving is very low.