I ordered two tree's fig trees last year. A Celeste and LSU Purple. They grew pretty well, but didn't ripen any fruit.
The Celeste put on a lot of figs but none would ripen. They would grow a bit, then fall off. They did that early in the season, then again later in the season.
The LSU Purple didn't put on any fruit until near the end of the season. A couple looked like they would ripen, but never did. I plucked the largest one after a freeze and the inside looked nearly ripe (but spoiled), but the outside was still green. So now I have doubts that it's really LSU Purple. I'll wait until I get fruit next year before I say for sure that it's not.