If Princess Lisa is seated on January 3, she will keep her seniority that goes back to 2003 (or maybe late December 2002—maybe her daddy named her to the Senate as a Christmas present), since her service in the Senate would be uninterrupted. But if she isn’t seated on January 3 immediately upon the end of her current Senate term, it will interrupt her service, and her prior service would count only as a tie-breaker if she is subsequently seated on the same date as another Senator. As I explained in post #21, Dan Coats’s 10 years of Senate service a couple of decades ago merely give him a step up on the other non-incumbent Senators being seated at the same time as he, but will not allow him to surpass the seniority of those who were already incumbents on January 3 (not even that of Mark Kirk, who was seated earlier this week because he won a special election for the term ending on January 3 and thus will be an incumbent when he is seated for the term beginning on January 3).
I’ve long found the tiebreakers you mentioned to be kind of cool. You get a whole bunch of Senators being seated on the same day, but the ex-Senators get the highest seniority, then the ex-Representatives, then the ex-governors, and those with prior service in those offices are ranked by state population in the prior Census. I believe that Chris Coons (no prior congressional or gubernatiorial service, and representing one of the least-populated states) will be last in seniority—unless Princess Lisa isn’t seated on January 3, in which case she will be last in seniority when she is seated.
Oops, my bad, I forgot that Coons was elected to fill Biden’s unexpired term and thus was seated in November. So the Senator who will be last in seniority will be Kelly Ayotte of NH, unless Princess Lisa isn’t seated on January 3, in which case Princess Lisa will be last in seniority when she is seated.
Excepting, of course, Joe Manchin, whose term as governor breaks the tie.
Your post #21 does explain why Princess Lisa is so anxious to get sworn in by January 3rd.