My dabbling in spinoff Who fiction has brought me to two other encounters between the Doctor and Lincoln, and I don't know of any others (though am ready to be enlightened).
Iain McLaughlin's novella Blood and Hope, in the Telos series of (frankly overpriced) Who novellas, brings the Fifth Doctor, Peri and audio companion Erimem to Virginia in early 1865; they gain the hostile attention of a deranged Confederate officer, but also assist in the reconciliation of one of the many families sundered by the war. The Doctor ends up assisting Lincoln in his famous walkabout in newly captured Richmond. McLaughlin, who invented Erimem in the BF audio The Eye of the Scorpion, rather neglects her here - she is, of course, as an African presupposed to be a slave - and instead looks at the background to his American characters. There are other flaws, but it is a well-meant effort to engage Who fans in the extraordinary events of the era in question. I have been pretty critical of Telos in the past, but this is one of their better ones.
If you ever go to Washington DC, I strongly recommend the small museum in the former Ford's Theatre building where John Wilkes Booth shot Abraham Lincoln on 14 April 1865. (The museum ticket also includes the house across the road where he died early the following morning.) The building itself has been reconstructed (after Ford's Theatre went bust, it became a government office which collapsed catastrophicallly, killing many budding bureaucrats), but both on my first visit as a seven-year-old and on my most recent visit at the age of 39 I found it a strangely compelling place.
Unfortunately Robert Ross's Big Finish play, Assassin in the Limelight, totally fails to capitalise on this setting. I was not wildly impressed by either of Ross's earlier Six/Evelyn/Knox plays (the one in Edinburgh with David Tennant being a deranged Scotsman, or the one in Brighton with Roy Hudd as Max Miller), and, alas, this is a desperate attempt to fit a time-travel drama about the very real events of this day. My complaint about the villainous Robert Knox remains that his means and motivation are pretty obscure. One of my many complaints about Assassin in the Limelight is that The Talons of Weng Chiang did nineteenth century theatre better, twenty years before (and that too was, er, not without its problematic aspects). The cliff-hanger to an early episode - where a key character is apparently poisoned early on the afternoon of the assassination day - turns out not to matter, because the poisonee was only pretending. The character in question is John Wilkes Booth. Which gives you some idea of the contempt the author is expressing toward the audience.
So, those of you who are interested in both Who and the US Civil War will find Blood and Hope entertaining and Assassin in the Limelight deeply annoying.