Mr Lagan, who sold his building materials business to Breedon Group for £445m last year, intends to expand the operation in tandem with his existing FastHouse brand.
Frame-Tech, which was founded in 2008, manufactures and installs more than 1,000 homes a year across the north of England and employs around 60 people.
It reported earnings of £3m for the year ended June 30 and turnover of £13m.
Lagan Investments, which bought the majority stake, says it intends to grow its market share collectively and will consider further acquisition opportunities. It expects the UK timber frame market to grow by over 25% to nearly £1bn by 2022.
Frame-Tech managing director Jamie Atkinson said the new investment would allow the business to expand its product offering and geographical coverage.
He also envisages opportunities to work closely with the FastHouse operation.
FastHouse recently completed 466 holiday homes for Center Parcs in Co Longford. Its factory produced five houses per day for the development.
