#3 G.O.D
While New Japan often puts on the best wrestling in the world, their tag team division lags behind other companies. However, that doesn't mean they lack talent in that department. While there's plenty of talent around, the top team in the company is definitely the Guerrillas of Destiny (Tama Tonga and Tanga Loa) and the 4 men would put on a very different type of match.
The G.O.D focus more on the brawling style, rather than the athletic, high-flying style that the others on this list. Combining that with the gritty style of LAX would make this for a classic on the New Japan Pro Wrestling stage.
In terms of companies that will get LAX's signature, the ROH/New Japan combination is in third behind AEW and WWE, but before they sign with one of those big companies, a few matches away from either in NJPW against GOD would be the best.