https://www.msisurfaces.com/blogs/post/2017/03/17/tile-style-easy-care-guide-for-slate-tile-flooring.aspx#:~:text=Mop%20your%20slate%20tile%20floor,or%20use%20a%20soft%20cloth.

Slate is dark. I doubt it can be lighted. Your floor is lovely. So much better than tiles pretending to be a natural substance, you have the real thing. It's timeless.

Slate doesn't get "refinished". It is what it is. You can have it professionally cleaned, and sealed with a glossy sealer if you like, but it's natural state is matte, and that's the better option for it to remain.

I'm in the pro-slate camp. Cleaning and resealing might lighten the floor if it's grimy, but don't expect a huge difference. It looks like it has lighter grout, so if cleaning lightens it up you'll see a marked improvement. My slate has standard gray grout which lightens up the look.