As far as I can read from the article, the lame-duck session happens only until the new Senators and Representatives take office (January 3rd).
From your link:
A lame-duck session of Congress in the United States occurs whenever one Congress meets after its successor is elected, but before the successor's term begins.
Also, it is clear that the previous POTUS is in office until the new one takes office (Twentieth Amendment of the USA):
Section 1. The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.
So, most of lame-duck sessions were held without a change of Presidency (for example, in 1950). In any case, until the new POTUS is sworn in the old one is still in office, so it would be his/her responsability to sign, veto or pocket veto any bill introduced by the Congress (either the "lame-duck" old one until January 3rd, or the "not lame-duck" new one after January 3rd).