I have never heard the LM but can speak directly to the Audio Mirror Tubadour III. I started out with a Node 2i and after a lot of research, including here on Audiogon, I landed on the Audio Mirror. It is highly regarded by many here and I'll add my voice to the list. It sounds amazing.
Others may be able to speak to the LM but wanted to give my two thumbs up for the AM.
Best,
Mike