I wouldn't bake it. The lining is probably held in place with glue, for one thing, and high temperatures could cause it to release toxins, or at least fail to work. Then there's the problem of what else is in the case; plastic, etc.Sorry to be discouraging after you've made your artwork, but I wouldn't risk it.
I used to do polymer clay art and I think I remember that it should only be done in a conventional oven, not a toaster oven in order to ensure more even heat. I might be wrong, as it has been several years since I worked with it. And I hope you are aware that once you have used utensils like baking sheets with polymer clay you should not use them for food ever again?
This would lead me to think that in something as small as a toaster oven vs. the larger interior of a conventional oven, you are risking accumulating toxic material that will later affect your food. Again, I'm sorry to be a downer about the whole project, but after I worked with clay for several years, I had second thoughts about the nature of the toxic exposure. The warnings say not bake it in the same room where there are pet birds, cause the fumes can kill them!
Talk about the canary in the coal mine!
To be honest I don't think you will have any problem with felt. Polymer clay cures at such a low temperature that paper does not even burn at that temp. Make sure to get an oven thermometer so that you can make sure your oven temp is correct.
I say go for it, I have baked fabric before with no problems at all. You can also make your eyeglass case with solid polymer clay, just use a flexible brand.
The safest answer is "when in doubt...don't". You don't know how flammable the materials are that make up the case. If you put it into the oven, I would not go over 150 degrees, and watch very carefully.At any sign of smoke, take it out.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.