The KL1 and KL4 heads have converter circuitry in the head itself. I won't try to guess whether it's boost, buck, or both. An E1L is pretty much just a KL1 head stuck on a E1 body. The E2L is a KL1 head stuck on a E2 body. The L4 is a KL4 head stuck on a E2 body.
The L1 and L2 lights are considerably different. The converter is in the body of the light, not the head. The head just has the optics/reflector, heatsink, and emitter. There are no "smarts" in the head of the L1 or the L2. The L1 has a Lux I (III?) in the head, and the L2 has a Lux V.
You probably shouldn't be swapping heads and bodies between the (L1,L2) and the (E1L,E2L,L4). If you do, you'll likely end up with a light that's in direct drive (no converter) or you have the output of one converter trying to drive the input of another. Either case is less than optimal.
The red Luxes have a relatively low forward voltage (Vf). Putting the red L1 head (which has no converter circuitry in it) onto the E1 body will direct drive the emitter. The Vf of the red lux is low enough that you get full output off a single 3 volt cell.
The white Lux I and Lux III emitters have a Vf that's typically in the 3.25 to 3.75 volt range. A single 3 volt cell does not provide enough voltage to overcome the forward drop of the Lux, and very little current flows. You will not get much light from a white Lux on a single cell. You will most likely fry it instantly if you try to drive it off an unregulated 6 volt source (two cells), but it may be very bright for that instant.
The Lux V in the L2 head has a Vf somewhere around 6 volts. If you run it without a regulator off a single cell, I'd expect you would get pretty much nothing out of it. You may get some light off two cells, but it is more likely the current draw would sag the voltage of the cells, and it won't be very bright. It is common to try to direct drive the Lux V off three lithium cells (Space Needle), but I would not recommend you try this with the L2 head because of insufficient heatsinking in the head. You also don't really know the Vf of the Lux V that Surefire used, and if it is unusually low it will draw more current than for which it is rated if you direct drive off three cells.
So, basically, there is no "problem" here. The L1 and L2 heads do not have regulation circuitry in them and they are not designed to go on E1 and E2 bodies. Red Luxes have relatively low Vf, and will go full bright off a single cell. White Luxes have a higher Vf than you can reasonably direct drive off a single cell (Lux I/III) or two cells (Lux V).