a great ceiling look would use real wood planks, either painted or sealed.


easiest material would just use 1/2" exterior grade plywood sheathing, painted. won't rot or warp, won't let critters into the attic, but will provide structural reinforcing against uplift (winds).

you can add a secondary ceiling material - mimic the plank ceilings above, or use a beadboard product. or, add 1x4 & 1x6 pieces to form a "paneled" ceiling.

Thanks for your suggestion. What about the walls?

not having a photo of your lanai, i'll assume it's not completely weatherproof.
same on walls - exterior grade sheathing, painted. you can dress it with beadboard paneling. more costly but you could use cement board (a brand name is Durock), which is used in showers behind tile.
depending on your style & the style of the home, you could use a nice siding product as the finish look (for an outside porch feeling). with a stucco home, perhaps introduce some decorative wall tiles.
technically, if the lanai has windows & doors, you could get away with using gypsum board (drywall, sheetrock) or a gypsum product called "greenboard" for damp but not wet spaces. but the humidity of Florida can still make them expand/contract if the lanai is not air conditioned.