I understand that we celebrated it on the last Thursday in November for almost a century, after Lincoln's Thanksgiving proclamation, until it was changed in 1941 to the fourth Thursday in November. But why did Lincoln pick Thursday, specifically?
Most likely borrowed tradition. New Englanders already celebrated a Thanksgiving (and some of the states that were settled by New Englanders) on Thursdays in November. But before Lincoln's Thanksgiving, they were appointed by the Governors of each state. The tradition of Thanksgiving on a Thursday in November, got its start in Massachusetts. The first real Thanksgiving was proclaimed in 1630 in the Massachusetts Bay Colony. It happened fairly regularly until around 1680, when it became an annual festival. Connecticut took the holiday up around 1639. It moved around a bit from colony to colony.
Interestingly, on the opposite end of the calendar for people in the Massachusetts Colony/State was Fast Day, which was typically proclaimed to be around the second or third Tuesday in April. It wasn't as popular as Thanksgiving, and eventually it became what Massachusetts celebrates as Patriots' Day.