(fyi, it's lanai)

As long as we're getting picky, there's also no such thing as a cement floor. It's concrete, of which cement is one ingredient.

Now, to your question. I wouldn't paint it. If it's in decent shape, I would have it polished. Otherwise, I'd probably use a concrete stain.

Here's an ideabook that might help: https://www.houzz.com/magazine/5-benefits-to-concrete-floors-for-everyday-living-stsetivw-vs~7977902

Oops excuse me....concrete. Thank you!

You could add a contrast concrete paint in a pattern for fun, interest and color. And then you could put a concrete finish in semi gloss or gloss.

Not this complicated but you can get a visual :)

It's a common mistake. Paul Newman's architect in "Towering Inferno" made that mistake and it's been a bugaboo of mine ever since.

I had 2 errors today....and I'm a good speller! I'm just getting used to having a "lanai"!