The last time there was a labor stoppage in MLB was in 1994, when the MLBPA went on strike from August 11, 1994 through April 2, 1995. However, that was a strike, so it is a little bit different than what MLB is currently going through with a lockout.
A strike is when the workers (in this case, the players) decide to stop working. A lockout is when the employer (in this case, the MLB owners) decides to stop labor until a new agreement for labor is agreed upon. The latter has not happened in MLB since 1990 and the 2021-2022 MLB lockout could unfold much like the 1990 MLB lockout.
The 1990 MLB lockout is something that can be learned from
The five-year Collective Bargaining Agreement (CBA) between the MLB owners and the MLBPA expired on December 31, 1989, and it expired without a new deal in place. Instead of enacting a lockout as soon as January 1, 1990 came, the MLB owners decided to carry on with business as usual.
After all, MLB and the MLBPA do not have to actually work with a CBA in place. An example of that is with the 1994-1995 strike. The players did not play with a CBA from the start of the season in 1994. After negotiations soured, they went on strike in August. They did not agree upon a new CBA until the offseason in 1996. Instead, they just operated under the previous agreement. This also happened in 2002 (more on that later).