The most stable and widely used custom ROMs for this specific model are:
: This is widely considered the most stable "modern" update for the samsung galaxy tab 3 lite smt116 custom rom 2021
Since custom ROMs don't include Google services, you'll need an MindTheGapps package (ARM, Android 7.1). installation guide for flashing LineageOS on this specific model? The most stable and widely used custom ROMs