Simple answer is no. The LWRCi is a piston driven system, where the AR-10A is "designed" to be a standard direct impingement system.
If he's already spent the cash on an LWRCi upper, he might as well go the rest of the way and pick up one of their lowers. Keep everything from the same manufacture.
By the way, I've handled a Reaper before, my son owns one. Pretty sweet. LWRCi makes quality stuff.