Mourinho won three Premier League titles with Chelsea over two separate stints, with Lampard one of his most important players at Stamford Bridge.
Lampard has now returned to the Blues as manager, leading them to a fourth-place finish last season in his first campaign in charge.
The pair are set to renew pleasantries on Sunday in a major Premier League showdown, with Tottenham entering the match in first place and Chelsea in third.
Though Lampard has plenty of expectations after Chelsea invested heavily over the summer, Mourinho has insisted that he faced more pressure during his time at Stamford Bridge.
“What I felt is that when I was in these clubs, there was huge pressure on me and now there is not huge pressure on the coaches of these teams. Put a little bit of pressure on them and leave us in peace, doing our job.”
Though he believes he faced more pressure than subsequent managers at Stamford Bridge, Mourinho also said that Lampard is currently under more pressure as Chelsea boss than Mourinho is at Spurs.
“When you are favourites, you know why you are favourites,” Mourinho said. “And you have to accept that and you have to deal with that kind of pressure and responsibility.
"I was at clubs which were, let’s say, champions in the market because of their powerful investments. I had to deal with that pressure. So now it’s not for me to deal with that pressure. It’s for others to deal with that pressure. That’s not for us.”
Mourinho contrasted Chelsea's major summer spend with Tottenham's more subdued transfer business, even though Spurs did spend on the likes of Giovani Lo Celso, Sergio Reguilon and Pierre-Emile Hojbjerg among others.
“It’s a different way of going into the market [at Spurs],” Mourinho said. “I’ve been at Chelsea before and I know the difference but I enjoyed very much to do this first market with Tottenham, to do that kind of wise market where, with less money, you try to give a good balance to the team, not to make mistakes, choose the right guys. I am really happy with what we got.”