I'm running mine on 2 x LiFePO4's that come off the charger around 3.7-3.8v. So far no issues.
Not certain about LiCo's / LiMn's though, might be a bit high at 4.1 - 4.2. I also did a few searches but couldn't confirm from the various threads I found whether the new E2DL can support these chemistries.
EDIT: Got my E1E today and can confirm that the head from the E2DL can run on the E1E body on a single RCR123 as well.