If you want to make your lanai an extension to your house, tile it. We are enclosing the lanai with double pane glass and had them add add concrete to match the level of our house floor. I just got done tiling the lanai with the same tile used in the house so when you open the patio doors, it looks like an extension of the house, no step down. I tiled our last screened in porch and it looked more finished than paining concrete.
The issue with a screened in lanai is to make sure it drains properly.

Tile in Lanai
 

We lived with a concrete floor in our lanai for several years before deciding to have the floor tiled. We selected Nickel Tile in Lake Sumter Landing to do the job, and they were great! We love the way the floor looks now and wish we had done this years ago. It changes the whole look of the lanai and makes it look more "finished." I should add, we do have our lanai enclosed, so that may make a difference in your decision.

I would think it is a personal choice! Mike

Be careful! A neighbor tiled his lanai (screened) with a smooth tile. During some months the humidity was great enough to condense moisture on the surface resulting in a very slippery surface. Based on his problem, I had T&D put a concrete non slip surface coating on the lanai. Good luck on your choice.

I enclosed the lanai - raised the floor - and tiled the floor. Great Lakes installed the tile floor -- excellent job. The tile is easy to maintain especially since you are coming in from the garden.

Have the cement stained and then epoxy, with or without the sprinkles. Tile is not only slippery but you have the grout to contend with .... mold/discoloring.

Best money you can spend is have it screened in - we had ours done by Martin Aluminum - very heavy duty acrylic sliders - I got fed up having to clean out the lanai every time it rained ....dust settles on the bug screens and when it rains you get liquid mud everywhere. I then had a glue down carpet fitted ....this was all over 18 years ago and it still looks great

Has anyone done Luxury Vinyl Plank with an enclosed Lanai instead of tile?

The room will have to be climate controlled and the LVP cannot be attached with glue or caulking. Those products expand and contract with the temperature and with sun exposure