A 3 gallon container for that size tree is way too small.

A fig is a very dynamic grower and will fill that small container with roots in one season. Then, the tree will be stressed. Personally, I would up pot that tree just as it starts to come out of dormancy in a container no smaller than 5 gallons. bigger would be better.

Planting the tree in ground, in full sun will bring about the best results. I would also pick a sunny spot in the yard and sink the containerized tree halfway into the surrounding soil and let the roots grow into the soil. Mulch the container up to the rim. Then, when tree goes dormant, sever the roots, lift the container, and store the tree, or, leave it right in the ground if you live in an area where fig trees get little or, no damage. You will have the best of both worlds, the tree will still be containerized if you decide on a different location, and the tree benefits from being grown in the ground, although containerized.

I have never grown any LSU figs, so I can't speak from experience. LSU figs were bred to do well in your area, and take the humidity. I don't see why they couldn't do well if containerized...however figs should get as much sun and heat as possible. Make sure if you containerize the tree, that the container is large enough to support root growth, especially, if you do not sink the container into the ground. If just grown as a containerized tree you must provide all the water and nutrients, including trace elements, granular limestone, etc. that the tree will need.

Your cultural treatment given to the containerized tree will be the deciding factor. The variety, not so much.

Good luck with you new tree, and happy growing.

Frank