Lankinen, who is expected to back up Juuse Saros after signing a one-year contract on July 14, also stopped all 13 shots he faced in 29:56 against the Florida Panthers on Monday.
The game was originally supposed to be played at Amalie Arena in Tampa, but the Lightning announced on Monday that they were postponing the game and temporarily moving their training camp to Tennessee because of the potential effects of Hurricane Ian.
Nino Niederreiter and John Leonard scored for Nashville.
Brian Elliott made 29 saves for Tampa Bay.
Niederreiter, who signed a two-year, $8 million contract with Nashville on July 21, made it 1-0 at 16:15 of the first period off a pass from Ryan Johansen.
Leonard, who signed a one-year, two-way contract on July 18, made it 2-0 at 17:22 of the third period.
