Senator Lodge argued that membership in a League of Nations would force us into alliances with countries that were of little importance to US interests, and that we could be dragged into a war to defend such countries whether we wanted to or not--that there would be treaty obligations we would regret.
This has not been the case with the United Nations outside of the Korean War, and we requested UN involvement in that example. The US has been much more likely to take unilateral action in fighting countries on its own, whereby our alliances in the UN and in NATO have consistently produced collective security and long term peace.
Lodge also argued that one way to maintain the United States in the position of a world leader in diplomacy was to continue the build up of a strong army and navy saying that military strength was a prerequisite to diplomacy.
I assume that you are talking about Henry Cabot Lodge and his arguments against the League of Nations. If so, I think that his arguments do remain relevant today and are typically used by people who do not like the idea of the US being involved with the United Nations.
Lodge's basic argument is that becoming a part of an organization like the League of Nations leads to a loss of American sovereignty. America could (he feared) be forced to do things it did not want to do. This is a major argument by those who favor a unilateral approach to foreign affairs. They argue (as when Pres. Bush was planning to invade Iraq) that trying to get UN approval for things limits American freedom of action and takes away from our sovereign ability to act as we choose.
The link below is to an essay by Ron Paul arguing that the UN destroys American sovereignty (not in military matters, but the point remains).