Look at the Lodge reservations: the key one is "2. The United States assumes no obligation to preserve the territorial integrity or political independence of any other country . . . under the provisions of article 10, or to employ the military or naval forces of the United States under any article of the treaty for any purpose, unless in any particular case the Congress, which . . . has the sole power to declare war . . . shall . . . so provide."
http://inside.sfuhs.org/dept/history/US_History_reader/Chapter8/lodge reservations.htm Congress, not the President.
True, some Irreconcilables thought even that was not enough. Senator James Watson (R-Indiana) in his *As I Knew Them* recalled how he had actually raised this point with Lodge:
"Senator, suppose that the President accepts the Treaty with your reservations. Then we are in the League, and once in, our reservations become purely fiction." (Watson, like Borah and other irreconcilable opponents of the League, thought that declaring that the US was not bound by Article X unless Congress decided on the use of force would not amount to much. Once the League's Council had voted to use force, with the US delegate agreeing, Congress, he thought, would not dare refuse; to turn down a President's request under such circumstances would greatly embarrass the US before the world.)
Lodge was not worried, replying with a smile, "But my dear James, you do not take into consideration the hatred that Woodrow Wilson has for me personally. Never under any set of circumstances in this world could he be induced to accept a treaty with Lodge reservations appended to it."
"But," Watson retorted, "that seems to me to be a slender thread on which to hang so great a cause."
"A slender thread!" Lodge exclaimed. "Why, it is as strong as any cable with strands wired and twisted together."
Again, Lodge may have been sincere about accepting the Treaty if his reservations were adopted. But the key to the reservations was that
Congress. not the president (acting through a US delegate on the League Council) had to consent to the US resorting to force.