That sounds like a fun project. I actually had a similar request some years ago, but it was for part of a tie-dyed cotton T-shirt.
Rather than putting the light source into the frame, I used a translucent white acrylic backing board in a frame design that could stand as well as hang. The customer said she would display the frame in front of a convenient light source, such as a lamp or window. Even a flashlight would work for short term viewing.
Extra frame dimensions may be required for internal lighting, as well as provisions to direct the light and prevent light leaks. Heat is an issue for incandescent sources and fluorescent ballasts. LEDs or neon lights burn cooler and, since the lamps are small and numerous, offer the advantage of better control of the light distribution.
Designing a frame with internal light sources is problematic. Wiring is necessary, which may involve some risk for framers who are not also electricians. By law in some jurisdictions, all wiring is to be done by licensed contractors. If anything went wrong with the frame's wiring to cause a fire, the framer could have serious trouble.