Fenix have never supported Li-ons in their AA/AAA lights.
I would stick with 1.2V NiMH, 1.5V alkaline, 1.7V Energizer L91 primary lithiums. There were problems with other no name brands of 1.7/1.8V primary lithiums (the batteries exploded).
Remember the L1P is an old light with a 1 watt emitter. CPF members who have successfully used 3.6V Li-ons in 1AA/AAA Fenix torches have done so with later lights that use 3 watt LEDs.