So I got it to work somehow.

First I tried to swap the satellites. Connected Spektrum satellite to the adapter and it didn't bind (no binding light, nothing).
Than I connected the Lemon RX satellite directly to sat port and it binded.
Than I connected the Lemon RX satellite to the adapter, got the binding light and that it went dark....again nothing but at least there was light for a few seconds.

So I than found out, that if the satellite is first binded directly through sat port and than connected to the adapter, I can see the binding light for a few seconds...

I was doing that back and forth, trying different combinations and than all of a sudden, both satellites binded (spektrum to sat port, lemon rx with adapter) and now everything is working.

I think that the problem is definitely in the adapter cable, because I also connected lemon rx satellite to AR7200BX FBL and it binded everytime.

I would be careful combining two different brand sats. Its generally not a good idea. Keep it either both lemon, or both spektrum.