Chelsea are at Old Trafford on Sunday for their Premier League kickoff.
Lampard told VG: "This was something he came in for, he got a really big boost, and then things got tougher. I think really, really you should give Ole this season and see what he can do now that he has had a run-up, brought players in and can implement his ideas in the long run.
"It's up to him to prove what he can do, just as it is for me.
"When you are the manager of a club like Manchester United or Chelsea, you may be strongly criticised. Sometimes it can be excessive. You have to be thick-skinned to get through it. It's an ordeal for all of us."