It might seem like it's an anachronism to have President and Mrs. Lincoln appear in a talking picture, when History gives us the year 1929 for Al Jolson's "The Jazz Singer". But you have to keep in mind that that's the real world; certain details will differ in Toobworld.
And the precedent for talking pictures to exist was established in 'The Wild Wild West'. Baron Hinterstoisser utilized a fake movie in hopes of bringing embarrassment to President Grant, as seen in a fourth season episode. And although it was a silent movie, the technology probably did exist to synchronize sound to it as well, thanks to Dr. Loveless. After all, as stated in one of the nine episodes to feature the diminutive madman, Miguelito apparently invented television!
So in a world in which there was at least one moonbase by 1970 and in which androids are hiding in plain sight, having a movie starring Abe Lincoln doesn't seem that far-fetched... for Toobworld.