22-year-old defender Alex has penned a two-year deal at Huish Park.
Manager Paul Sturrock said: “I am delighted to secure the signing of Alex. He is a natural talent that has played fairly regularly in League Two, I feel he has massive potential and I hope we all get to see that potential.”
Lacey penned his first professional contract at Luton in 2010 and has remained at The Hatters throughout his career to date.
He has spent time on loan at Cambridge City, Thurrock, Eastbourne Borough and in 2013 spent time on loan at Eastleigh.