I recently read that Garmin is warning that the higher voltage lithiums could damage some models of GPS's. That is why the latest update to the GPSMAP 60CSx actually has the lithium battery option (in the software) removed.
I found this at Garmin's Support site:
"Not all lithium ion AA batteries will work with our GPSMAP 60 and 76 "x-series" devices as they have too high of an output voltage. Typical AA batteries have a voltage of 1.5v each. Some lithium ion AA batteries put out 1.65v or higher. Our units will only accept power from batteries that output less than 1.65v.
If using Lithium-ion batteries and the gps will not power on or will shut down quickly after being powered on, the high voltage could be the issue. They will need to be drained a little to be in the operative range in the unit. Use a flashlight or other device that uses AA batteries to drain some power from the batteries."
The info that came with my wife's Streamlight Survivor LED and our Streamlight ProPolymer 4AA LED lights both say to "Use only alkaline batteries". I assume this is also a voltage issue.
My Princeton Tec lights specifically say lithiums can be used.