Having been tagged as title contenders at the start of the season, Chelsea have been handed a brutal reality check in recent weeks, with the club recording just one win in their last six Premier League games.
That run has included four defeats along the way, seeing them slip to ninth position on the league log.
Given that Chelsea spent over £200m on summer recruits, Lampard has come under pressure to turn things around.
Grant, who led Chelsea to their first ever Champions League final in 2008, with Lampard as a key member of that side, is adamant his former player has enough experience to right the wrongs at Stamford Bridge.
"About the current situation I can say only this. You need to be strong when things are not going well, when things are going well everyone is a genius and knows what to do," Grant said in an Instagram post.
"But in the situation like this when things aren't going well you need to be strong, look for solutions and show a lot about your character."
Grant added: "What I can say to Frank and the others at the club is be patient, and more than this do whatever is necessary to do that's for sure. Two things: never lost it even when things are going well, don't lose your fighting spirit at the highest level.
"And second, don't lose what you have here [points at head] you need to think right and look for solutions. If you do that then everything will be okay because the quality is there and there is a potential like there was [at Chelsea] in my time."
