It's really good to hear that no one has yet experienced any problems running the L0Dce on 10440 3.7V Li-Ion Rechargeable.
However the XLamp XR-E LED pdf
Data Sheet posted at Cree.com says the Max current for the Cree XR-E is supposed to be 1000mA -
In
Fenix L0D-CE Comparison Review I got measurements of -
Current draw -
10440 Open-Circuit voltage = 4.03V
Medium = 0.38A
Low = 0.17A
High = 1.11A
which means the current drawn on High exceed the maximum rating by about 11% (others have reported similar readings)
This does not necessarily mean the Cree LED in the L0Dce will blow up or suddenly burn up - as the numerous reports of no problems clearly shows.
BUT there is the probability that the LED's life may be shortened with frequent and continuous use of over max current - eg: 10440 on High.
Might want to read Cree's Lumen Maintenance statement
from their pdf
Data Sheet -