The former Chelsea and Everton manager expressed his sympathy for Wayne Rooney after beating his Plymouth side 4-0.
Coventry inflicted a huge blow on Rooney, whose team are bottom of the table in the Championship.
"I know the challenges of each job and you only know when you're in it," Lampard told talkSPORT post-match.
"Wayne obviously has his career behind him and now his management career as well, which he's gone straight into. There will be challenges for him there.
"It's not for me to comment on that, I'm very happy with us today. I always wish Wayne well because he's a proper football person.
"Again, there's challenges so people have to understand he's working. I hope to see him do well because he's a young English manager with a lot to give and that continues to be the case."