The 115th Congress comes to a close at noon Jan. 3 and lawmakers haven’t wound up the items on their lame-duck tax agenda—adding tax policy to the growing list of issues the new Congress will have to deal with at the start of 2019.

The list includes extensions of expiring tax breaks, fixes to the 2017 tax law, measures to rework certain Internal Revenue Service functions, and provisions to help taxpayers save more for retirement.

Some, if not all, of these items could be taken up by the...