On what grounds did henry cabot lodge and other republicans reject the league of nations?

I had no idea, so I googled it for you, and someone on yahoo said, "One school of thought blames Lodge and the Republicans for the US failure to ratify Versailles or join the League. Wilson did much to sabotage the effort himself. He refused to allow any Republicans on his delegation to France. When Wilson returned in 1919 he refused to make any concessions to the Republican controlled Senate, instead going on a speaking tour to convince the people directly. This all blew up in his face in early 1920, when the Senate rejected the entire package. The US eventually made separate peace treaties with the former Central Powers. In any event, the enforcement powers of the League of Nations were so weak as to be unable to prevent war."

I have no idea if this helped, but I hope so :P

Acceptance of the League of Nations required a Commitment to the treaty of Versailles. I'm guessing they Didn't Commit to it