The answer is CAN. U can ask the tailor to make a reversible suit. The suit does not having lining. U can have either regular lapels or notch lapels. The drawback of such suits is u cannot make very structured shoulders because it has to be able to be worn 2 side. And such suits are a little on the heavy side. It could be warmer too. But unless u can make it without using very thinck wool, then it might be wearable. The only time i have seen a reversible suit jacket is made by Commes Des Cargons. One side is regular black dress suit jacket, and when u flip it inside out the other side is dark blue in color and has a tribal print on it. I saw it once at some bundle shop. They were asking a lot for it. You could still see some beng sold in Japan Ebay by the same brand.

The only problem now is finding a tailor that would make such a suit for you. And how much you are willing to pay for it. But u stirred my long curiosity on the question if any tailors here willing to make one. Hell such jackets exists in movies. i think the first time i saw such jacket is in Mission Impossible tv series 1970s' one. Ok time to hit the tailors for pricing and feasability.