Two AA give 3 volts , LiFePO4 has a nominal voltage of 3.2 volts. When I bought my lights, Fenix was offering a kit (that is what I actually got) which included, a diffuser, the L2D and the tube of the L1D, so yes, the L2D and the L1D both use the same head.
Thanks the HKJ reference, I'll check...