I have a Linear FS20Z-1 which is very similar to the LFM-20 hooked up to my LifeMaster and it works fine. Here is how I set it up:
Since the relay needs 110 power, I decided to install it in the ceiling using the same power going to my opener.
I pulled out the single junction box and replaced it with a double gang and put the original outlet back and the Linear beside it.
I disconnected opener wire from the LiftMaster and then twisted those two wires to the Linear’s blue wires.
I used an extra piece of telephone wire I had laying around and twisted a pair of those wires to the blue wires and then capped them.
I then hooked up the other end of the telephone wire to the opener.
In my case both the Linear relay and my original wall switch work to open the garage. I hope this helps your situation.