I've got a lot of unprotected 18650 cells, so I like to run those wherever I can. I've got a couple custom bodies that I use for E series heads. I'm not sure if they count as Surefire lights, since only the head is Surefire.
I've had good success using li-ion in my U2. The body is one of the older styles which accept an 18650 cell. It didn't even have the plastic tube in the battery compartment. This light runs great on li-ion. I've never seen it overdischarge an unprotected cell.
The KL4 head works well too. I don't know if it will overdischarge the cell if left unattended. There is a fairly noticeable drop in output once the cell gets low. It's almost like it drops into moon mode.
I have mixed feelings about the KX2 head. It runs fine on li-ion, but doesn't seem to stay in regulation for as long as I would like. Once the cell voltage drops below 3.9 or so, the output starts to dim. The dimming is very gradual, and the KX2 continues to produce light for many hours. I do not think it would be possible for the KX2 to overdischarge the cell. I just wish it would run in full regulation for longer.
I've run KL1 heads on li-ion too. They run great, but they will suck a cell dry. I don't think you would even notice a drop in output before it was too late. I ended up selling off all my KL1 heads. Of course, a better idea might be to use protected li-ion cells instead. Then you should be able to safely run the light until the protected circuit kicks in. You wouldn't have to worry about damaging the cell. Of course, you might end up with a light that just clicks off when the cell is nearly done. In some situations it's better to have a light with gradually diminishing output.
I've also run the ExE head with a Lumens Factory 3.7 volt halogen lamp... but you asked specifically about LED lights.