She was born Laura Lengthorn on 2 November 1983 in Great Yarmouth. She attended Albany High School, Chorley, which is now called Albany Science College. In July 2007, she married Danny Massaro and became Laura Lengthorn-Massaro. She subsequently dropped 'Lengthorn' from her name.
She won her first top-level title at the German Open in 2004.
Massaro also won the British National Squash Championships in 2011, defeating Jenny Duncalf in the final 7–11, 11–9, 7–11, 11–7, 11–2. She had previously finished runner-up at the championships in 2008 (losing in the final to Alison Waters 11–6, 7–11, 8–11, 9–11).
At the 2010 Commonwealth Games, Massaro won a Silver Medal in the women's doubles (partnering Jenny Duncalf).
Massaro won the British Open in 2013, the first English woman to do so in 22 years at the time.
Laura's sponsors include 305SQUASH for clothing, Head for rackets, Asics for shoes. She is also sponsored by Proto-Col and CourtCare.