We are planning on extending our lanai soon. We checked with Sumter county tax appraiser about this and he said if you enclose or extend, then add heat/AC, your taxes go up. Your existing screen lanai is taxed at 45% of its value.

Enclosed our Lani just a year ago and at the time contemplating adding air.
We have found by leaving the sliding glass doors open and ceiling fan on the temperature is very comfortable summer and winter our ac/ heat system handles it very efficiently.
We have also added window shades to minimize solar heating