All of the following information is based on the older L1 (I do not own the latest L1).
The parts of the E1L and the L1 are not designed to be interchanged, as far as I can tell.
With the E1L, the regulation circuitry is all in the KL1 head. The body of the E1L is basically just a battery holder and the tailcap is a clicky tailcap.
With the L1, the regulation circuitry is in the body and the LED head is "dumb". You could put the head from the L1 on the E1 body but this essentially direct-drives the L1 head so the light output will directly depend on how much juice you have left in the battery.
The L1 tailcap will not fit on the E1L and vice versa.