Silva took to Instagram to thank Lampard for his help during their short stint together.
"I would like to thank you for everything you and your committee have done for me since the day I arrived," Silva wrote.
"As I told you, it seemed like we had been together for 10 years!! Thank you for everything legend."
Silva was one of Chelsea's arrivals in a summer spend of over £200million under Lampard.
Tammy Abraham, who was Lampard's main striker in his first season in charge, posted a picture of them together, writing: "A role model, a mentor & a great manager. Thank you Gaffer."