Q.Fig Tree
I ordered two fig trees online recently. One is a Jack’s Black and the other is an LSU. They are in planters, both have the same soil composition – potting soil, manure, perlite. Both are in the same size pot and get the same amount of water and light. The Jack’s Black is doing extremely well and growing new leaves. The LSU has done nothing. When I got it, it had 3 small leaf buds on it. One month later, it still has the same three buds that have not grown at all. No other leaves are forming on it either. It seems to be dormant. What should I do?

Jack's Black fig is rated from zone 5 and LSU is zone 7.
I suspect it has not been warm enough for your LSU Fig tree to grow.
Try moving your plant to a more sheltered and warmer area of the garden.
https://www.gardeningknowhow.com/edible/fruits/figs/how-to-grow-figs.htm