The 20-year-old has impressed this season and a number of sides, including Premiership outfit Middlesbrough, have been keeping tabs on the youngster.
However, The Hatters have swooped after agreeing a £300,000 fee for the youngster - a club record sale for Macclesfield.
"It is inevitable at a small club that good players move on and, given the problems being faced by many clubs today, I'm pleased that we have been able to benefit from a positive move in Rickie's career," said Town manager Dave Moss.
"I certainly wish the lad all the best. The squad I have is still strong and, with the board's support, I hope I will be able to improve it over the coming months so that we can make a realistic challenge next season."
Stockport have been looking to bolster their squad and have landed Lambert, after they failed with a bid for Doncaster Rovers striker Andy Watson.
The 23-year-old impressed Stockport's director of football Colin Murphy in recent weeks and manager Carlton Palmer made a bid, after checking on him last week.
However, the South Yorkshire club have shunned a six-figure offer.
"We don't want to lose Andy but we're realistic here at Doncaster and if someone came in with an offer of £1million, Andy Watson would be on his way," said manager David Penney.
Meanwhile, County have confirmed that midfielder Ali Gibb has been placed on the transfer-list at his own request.
