At times on second serves I hit an offensive lob over the net man's head. He's standing too close, and there's no way he or his partner can take it out of the air. His partner has to run across the whole baseline and hit a lob himself 9 times out of 10.
And to answer the OP it should be automatic to switch in this scenario. When I'm the net player, and the lob is over my head, my usual practice is to slide over to the open side and stay at about the service line until my partner hits the ball. From there we decide to advance, retreat, etc. but at least we have both sides of the court covered.
A lob hit down the middle would be another story… that would be a better case for calling out switch or stay.