Not sure it will work well. A LP mahogany body may be too dark for the PU so you will definitely not get the same tonally quality as from an Axis, if that is what you are after. Bear in mind also that the Axis bridge PU is F-Spaced, the LP bridge is not, I stand corrected however.
I know that some of you guys will jump at me, but the body wood has near to zero impact on the sonic result in an electric (!) guitar.... #smartass #italkedtotheluthiers #italkedtothetech