In 2001, Lapham signed on for Swindon Town's youth. The player received praise by youth coaches Iffy Onuora and Ian Woan. In December 2004, Lapham was all set to leave his football career for plumbing after being told a professional contract with the club was unlikely. However, due to injuries to Sean O'Hanlon and Steve Jenkins in April 2005, Lapham was in contention to make his first team debut. Despite Jenkins recovering enough to be named in the starting lineup against Huddersfield, Lapham was given a debut. Lapham was one of 1/4 youth teamers to make their debuts due to Rory Fallon and David Duke being sent off. The match finished 4–0 to Huddersfield.
Lapham once again received praise for his ability from Swindon Town manager Andy King, who said he "defended magnificently" when helping the youth team win the Youth Alliance cup. He was given another chance to shine for the first team at the end of the campaign against Chesterfield in a 1–1 tie. Due to Lapham's impressive performance he was rewarded with a professional contract on 6 June 2005 as well as winning the club's Young Player of the Year award.
The following season Lapham had gained a knee injury preventing him from making and impression for the start of the season. After not making an appearance in the first half of the season, former youth coach and new Swindon Town manager, Iffy Onuora, sent him on loan to Cirencester Town for 3 months. Upon his return to Swindon Town at the beginning of May, he was informed he was surplus to requirements at the County Ground. He went on to sign a contract with Cirencester Town.