Not much, it is a fork. The things added by /e/ repos are separate. They add some complexity, so if one wanted to test progressively one might try pure lineage4microg, if it works and MicroG does not prove a blocker, then add /e/ repos and try again.
I do not use docker and that tends to hide what you are doing if experimenting. I would use this method [HOWTO] build /e/ the (full) classic way (no docker, no scripts, just 'make') to do the test you are contemplating.
As I read further, I can confirm that the emulator bits from LineageOS are included in the /e/ build; if these bits are missing in other non Lineage derived custom ROMs the emulator proposal would not work for those custom ROMs, I guess.
I have to wonder what you expect from the emulator? It will not actually work, it might be useful for an App developer to test his App against the emulator to see it looks ok, but probably be limited in testing its functionality, idk.