I run my KL1's (E1L+E2L) on Li-Ions, R123's.
They come off the charger @4.20v, gives a slight boost to a single cell setup with the higher voltage. However, i get just over half of the run time of regular primaries, and your using a battery that is less then half of the capacity of my R123's, so i would expect about 15-25 minutes or less before it cuts out.
YMMV.
Hope this helps.
IF