The agreement marks the culmination of a year-long search by the Scottish firm for a partner to help it broaden its services and expand in England.
Everwarm, which employs 250 staff at offices in Bathgate and Bedford, becomes the fourth business to join London-based Lakehouse since 2011.
Lakehouse said the four shareholders in Everwarm, chief executive Michael McMahon and directors Kennedy Saunders and Lydia Graham, will hold stakes in the enlarged group, with the Everwarm management team staying in place.
The Everwarm brand will continue to trade in Scotland.
Everwarm installs energy-saving products in homes and businesses, such as cavity wall insulation, air source heat pumps, loft insulation and solar panels, and has served 45,000 clients since 2011. The company booked pre-tax profits of £6 million on turnover of £46m in its latest financial year - its third year of trading.
Mr McMahon said: "Our merger with Lakehouse is the result of a year-long search for a suitable partner. Rather than a corporate investor, we were looking to join with a business that would allow us to diversify our range of services and help us build on our success to date. We have found a like-minded partner in Lakehouse, and joining the group will allow us to offer more to our clients.
"Now, we look forward to growing our English operation within the Lakehouse group and bringing a wider asset management offer to clients in Scotland."
Lakehouse, which is focused on the social housing, education and public buildings sectors, reported a 48% increase in pre-tax profits to £7.1m in its last financial year. Turnover rose by 24% to £190.6m.
Executive chairman Stuart Black said: "Sustainability is a fundamental plank of our business and we'll be drawing on Everwarm's impressive delivery record in Scotland to expand our retrofit division.
"There are huge opportunities in London and south-east England - a domestic market which is remarkably immature in terms of retrofit and energy efficiency.
"The merger will allow Lakehouse and Everwarm to leverage each other's strengths and service offerings across the areas we cover."
Neil McGill, of BDO, which advised Everwarm's shareholders on the deal, said the firm is now in an "even stronger position to continue to grow within the energy-efficiency market and to develop its service offering to clients."