Tuesday evening's tie will mark the first time that the two men have met in a managerial capacity, with Lampard winning three Premier League titles under the Portuguese during his playing days.
The 40-year-old acknowledges that no manager is ever truly safe from the sack, but believes that the Red Devils will think twice before making a change in the dugout if their problems continue.
"The fact is, any manager who goes beyond three years [in one job] now is probably the exception to the rule," he told reporters at his pre-match press conference.
"I don't think it's anywhere near specific for Jose - that's the nature of how the game has gone. Of course in management, we know we're all sackable at any moment.
"I am, he is, every manager is. But at the same time, when he's had the success he's had, as long as he goes on, people are going to want Jose Mourinho as their manager."
Lampard has lost three of his first 11 games as Derby manager.