If it were me, I would not.
Lexan, while a cool material, is still highly prone to Scratching and those scratches are very diffficult to remove. It you want a crazy shiny black floor I suggest you
purchase a purpose mixed floor paint, our local supplier has one they
call "Tuf Tread". Use 5mm / 1/4"
MDF as your flooring. You're going to want to fill and finish screw holes if you want an unbroken look to the floor. Once everything is beautiful mop with several applications of "future" floor finish using an impeccably clean Swiffer, or lambs wool
polyurethane application thingy. You will have a HIGHLY shiny surface. Because it is an Acrylic finish it is slightly flexible and it wears quite well. IF you get scuff marks then grab a
bottle of Windex, or ammonia in a spray
bottle <Windex is easier on the nostrils> spray the area let it sit for a minute than mop with the Swiffer or just mop over the area with more Future.
One issue I have noticed with Future is that,, because of it's more plastic nature, it tends to be grabby. Dancers don't like it and it doesn't like things sliding. I have not come up w any good way to refinish
Polyurethane over the course of a shows run or I would suggest that.
Good Luck and Welcome aboard!