A wheat variety designated LSPA15-HD307, the plants and seeds of wheat variety LSPA15-HD307, methods for producing a wheat plant produced by crossing the variety LSPA15-HD307 with another wheat plant, and hybrid wheat seeds and plants produced by crossing the variety LSPA15-HD307 with another wheat line or plant, and the creation of variants by backcrossing, mutagenesis or transformation of variety LSPA15-HD307 are disclosed. Methods for producing other wheat varieties or breeding lines derived from wheat variety LSPA15-HD307 and to wheat varieties or breeding lines produced by those methods are also provided.