It certainly is possible to enclose an Echo inside a metal box if you can find someone to manufacture such a box for you. My first thought is try using an ammo box like this one on Amazon:
https://www.amazon.com/50-CAL-Ammo-Can-Surplus/dp/B00ICR9LBWYou should verify the dimensions to make sure an Echo will fit inside.
And since you want to add external LEDs for the lights on the Echo's ring, you might also want to add an external wire to extend the WiFi antenna. A search on Amazon for "external wire antenna" reveals many options.
Third, a metal box will make it near impossible for the Echo to hear and understand you. And you might have difficulty hearing its responses. You should consider an external mic. Or at the minimum drill a bunch of holes in the appropriate places for the mic on top and the speaker at the bottom. There's no telling how the Echo might react to the environment inside the metal box. It could feedback on itself making it entirely unusable.
All this is going to be A LOT of work. Is this project really worth all the trouble?