He means Joseph Lister, of course, the guy who had the radical idea that surgeons ought to wash their dad-blamed hands before they operated on people, and that in general being dirty was bad for you. Since Lister's breakthrough was in 1865 and he left Glasgow in 1869, that's probably the period when the doctor was studying with him in Scotland.
But as we know, the Doctor lies. Why would he have studied with Lister? Would a centuries-old Time Lord need to learn about how germs are spread? Perhaps it's more likely that the Doctor was there giving Lister hints...
But could he be telling the truth? Bell and Lister were contemporaries, and the ever-curious Second Doctor could have been drawn to hanging around with both of them. And given the trouble he had controlling the TARDIS in his first and second lives, he might easily have been stuck in Scotland for a few years.
Just a theory.