She had died on Thursday from pneumonia and Lampard was missing from the line-up against United as a result.
Grant does not know whether the influential midfielder will return for the return leg of their semi-final against Liverpool on Wednesday.
"The players have a lot of sympathy for Frank, you saw that after the first goal," said Grant. "We are a big, big family, the staff and the players and what has happened to Frank makes all of us very sad.
"From me I send my sympathy to the family from everyone here. We will leave the decision about Wednesday to him. I will respect any decision he makes.
"Football is exciting but there are things that are more important. I say to the players that on the way to excellency you need to be human, so I think we need to respect what has happened to him.
"Frank wants to play all the time. When I put him on the bench after many years of playing he didn't feel good with it. He wants to play but we need to respect his situation."