Van Gaal has paid the price for a disappointing, trophyless season by having his contract terminated one year earlier than planned and Heynckes this week agreed to take over from the summer and Lahm says his club have got their decision-making spot on.
"That is the way things are when you are at FC Bayern - if you are not successful, then you have to face the consequences and I think that is absolutely right," he told the Bild am Sonntag newspaper.
"FC Bayern have the aim to be the number one all the time and always win titles. If that does not happen, then questions are asked of everything and that is what has happened this season.
"It has nothing to do with fairness, but those in charge at FC Bayern make decisions which make it clear to everybody that we cannot go on like this. That is right."
Lahm has already worked six weeks under Heynckes at the end of the 2008-09 season and is looking forward to reacquainting himself with the current Bayer Leverkusen boss.
"He gave us our enjoyment back and we won four of the five games under him, drawing the other, so we were very successful and that is why the appointment of Heynckes is a good decision.
"I have a good feeling about Heynckes. He knows FC Bayern and all of the decision-makers very well and it is certainly going to work out with him. Bayern Munich and Jupp Heynckes - that sounds like a winning team."
However, before Heynckes arrives, Bayern must bring the season to as successful a conclusion as possible. They are currently two points behind third-placed Hannover with seven games of the season remaining.
Were the campaign to end now, Bayern would only be playing in the Europa League next season and Lahm admits nobody at the club wants to contemplate that.
"The Europa League is smaller and less attractive in every respect," he said. "The cities, the clubs, the stadia, the attendance figures - everybody who works in football thinks this way.
"At FC Bayern, we want to measure ourselves against the best in the world, not with the leftovers from a party."