The Yellamen became the only Hellenic League side to progress to the last 32 of the competition after beating Colliers Wood 3-2 on Saturday.
A brace from Ben Knight and a low drive from Dave Hoar secured Ascot United's place in the fourth round, although they were forced to endure an agonising finale after the hosts pulled a goal back with 10 minutes remaining.
Lamb told the News: "It's massive for the club and the community. Our cup run is getting people of all age groups at the club interested.
"We want to try and get as much interest and get a coach-load of supporters because it really does make a difference."
He added: "We're the only Hellenic side left in the competition so we're flying the flag, which is great."
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