On Feb. 10, David Letterman stopped by “The Tonight Show Starring Jimmy Fallon” while his former bandleader, Paul Shaffer, and his World’s Most Dangerous Band filled in for the Roots.

In IMSA, the team uses the BMW Team RLL tag. Letterman, an Indianapolis native and longtime IndyCar fan, first purchased part of the team in 1996. He’s a regular at each year’s Indy 500 ...