Lodge primarily felt that the United States entry into a world organization would handcuff its capacity to be autonomous. Theoretically, he might have been on to something. Yet, in practicality, we can see that this is not the case. The United States is part of many world organizations and its desire to act unilaterally or in its own interests is not compromised. As part of the United Nations, the United States has not been pulled into any foreign conflicts from which it could not extricate itself. At the same time, when the United States unilaterally desired to go into Iraq, no nation stood in its way. No nation handcuffed it. Lodge felt that the US commitment into international organizations would cause it to have to respond to every crisis available. This has not been the case. The US has not responded in areas like Rwanda or the Sudan. It has steered clear of situations where there has been horrific crimes against humanity and moments where "democracy has been threatened." The United States has been able to retain its autonomy in these settings. I think that Lodge's conception of international organizations was seen as much more binding than what is actually present. The United Nations is not a dominant force that demands immediate capitulation. It is perceived as more of a peacekeeping organization that has some military capacity, but is extremely limited in this light, allowing nations like the US to not be overly committed to it. Lodge might have been happy with such a construct.
Lodge's main objection to Article X of the charter of the League of Nations (I assume that's what you are talking about) was that it could pull the United States into wars that were not important to it. This was because all countries were required to come to the aid of a country that was attacked. This could mean, for example, that the US would have been required to fight Russia when it invaded Georgia not too long ago.
I do not think that this is all that relevant today. The reason for this is that the US can avoid participating in any UN action simply by vetoing the action or by refusing to send troops. The UN cannot force the US to participate. This is a real weakness of the UN and one reason why many people think that the UN is pointless.
Because of objections like those of Lodge, the UN cannot force the US to participate in any actions so there is no need to fear the US being forced to fight in a war that it does not want to engage in.