Sherwood was in charge of Spurs during Lamela's first season at the club.
Speaking on Match of the Day 2 last night, Sherwood insisted that no-one tries harder than Lamela, who scored and assisted against the Red Devils.
Spurs paid a club-record £25.8 million to sign Lamela from Roma in August 2013, but the Argentine struggled to find his feet initially.
He scored once in 17 appearances throughout his debut season in England, in which Sherwood replaced Andre Villas-Boas in the hotseat.
That tally was increased to five under Mauricio Pochettino the following campaign, but with five games still to play in 2015-16, Lamela is already into double figures for goals.
"No-one tries harder than Erik to fit into the Premier League," Sherwood told the BBC's highlights show. "He works his socks off every single day in training. I think he’s got stronger physically and mentally."
He added: "I’m really really delighted for him because if anyone deserves it, he does. It was a big price tag when they brought him into the football club and now he’s showing what he’s really worth."
Dele Alli gave Spurs a 70th-minute lead at White Hart Lane, before quickfire goals from Toby Alderweireld and Lamela secured an emphatic victory for the hosts.
Alderweireld's strike arrived courtesy of a Lamela set-piece and Sherwood commented: "If anyone can take free-kicks off Christian Eriksen they must be very, very good."
Spurs fans were also impressed by Lamela's display, with 42.68 per cent voting him as Sunday's man of the match.