So if you really want an LDP-style party in America, you need to first think about how it came to be in the first place. It certainly could have come to exist in some alternate scenario, sure, but as they say, the devil is in the details.
Like most scenarios where the two-party system is broken, it would require the abolition of the electoral college. But I could definitely see a near future big-tent party in the US having similar goals to the LDP: market-oriented privatization and administrative reform, bigger military and more involvement in the Asia-Pacific, and businesses' interest in free enterprise tempered by some protectionism. The LDP's degree of government control has always been somewhat stronger than their Western counterparts', though, and I would expect that to be true in comparison to a US LDP.