The floor
Painted or textured concrete that has chalked, cracked or simply worn through. The choice is between resurfacing, tiling with something rated for outdoor use and wet grip, or laying pavers. Whichever you pick, the question first is whether the slab underneath is sound, because putting a new surface over a slab that is moving buys you a year.
The ceiling
Often the quickest visible win. Original lanai ceilings tend to be stained soffit panels or tired painted timber. Replacing or refinishing them, adding proper lighting and a fan sized for the space, changes how usable the room feels far more than the cost suggests.
Lanai remodeling: screen, enclose, or condition
The decision that sets the budget. Rescreening keeps it an outdoor room. Enclosing makes it weather-tight but not necessarily conditioned. Making it part of the house is an addition, permitted and built as one. All three are legitimate; they are not variations of one price.
While you are there
A conditioned lanai is an addition under the Florida Building Code. Outdoor circuits and a GFCI supply, a gas run if there is going to be a grill, and the threshold where the sliding door meets the deck. That threshold is where water gets into the house, and a lanai remodel is the moment to fix it.