Try a 3.7 v 17670 battery which should fit an L4. Some of the older models may require some boring out to fit the battery. Mine works well with a 17670 battery.
from 4V-3V [rechargeable discharge] the driver operates as a boost circuit
if using 2xcr123A [6V] the driver, instead of bucking, operates as direct drive, but for a very small time before going into boost, so little difference is noticed during primary discharge and rechargeable discharge in terms of relative output
if your using rcr123A [full charge 4.2V] at direct drive thats 8.4V instead of the original intended 6V