The L1D-CE runs ok on a 14500, although you'll only get turbo and strobe until the voltage drops quite a way. The head is the same as the P2D-CE, which uses a single lithium cell. You should get about the same run time as a P2D-CE using an RCR-123 cell, which has about the same capacity as a 14500. I measured 31 minutes on Turbo with the P2D-CE/RCR-123A combination.
c_c