The consideration for the initial investment is £9.1m in cash with 50% payable on completion and a further 50% payable during 2017.
The agreement also includes put and call option provisions from the date the Group First 2018 audited accounts are filed at Companies House, which if exercised would increase LSL's investment to up to 100%.
The additional consideration payable for the remaining shares would be calculated on an earnings multiple of between five and six times EBITA plus excess cash in the business and is capped at a maximum of £25m.
The management team, who retain a 35% interest, is led by Paul Maston who founded the business in 1988 and will continue as CEO of GFL. GFL reported profit before tax of £0.7m for the year ended 31 May 2015, at which date it had gross assets of £1.8m.
Ian Crabb, LSL Group CEO, said:
"This investment supports LSL's strategy to grow long term profitability in the provision of residential property services in the UK, by identifying value enhancing opportunities. Further, the investment strengthens LSL's relationships with its key housebuilder clients."
