I believe that it is possible if one skips the inter-terminal train and directly walk from 2F to 2E-L through the concourse.

The tricky part will be returning from 2E-L to 2E-K, you will have to take the train and then pass through security check again: from the lounge 2E-L, instead of going down 2 levels back to the departure level, you need to take the stair (not the elevator, as it only goes from departure level to lounge level) to go down only 1 level to the arrival floor, and then take the escalator from there to go down 2 more levels to the train platform.

To find the stair, you exit the lounge and it will be the first exit on the right; the elevator is further deep in the corridor.