The acquisition of Auto Windscreens, from HSBC private equity, will expand the range of motoring services offered by the RAC. Lex paid £42m for the equity, and took on £70m of debt.
Andy Harrison, chief executive of Lex, said: "This acquisition fits like a glove with the RAC ... it's a fantastic opportunity to develop the RAC. Our aim to provide a cradle-to-grave range of motoring solutions."
The RAC, bought by Lex two years ago, already offers car insurance and owns the BSM driving school.
The AA, owned by Centrica, is believed to have made an offer worth around the same amount of money but the Auto Windscreens management chose the RAC for cultural reasons.
"They didn't want to be part of a vast organisation like Centrica. They preferred to be with a smaller, more nimble company," said a source close to the deal.
Auto Windscreens was put up for sale some six months ago and Lex has been in exclusive talks with the company for about a month. Last year, the business made a pre-tax profit of £4.1m on turnover of £91.8m.
Auto Windscreens is the number two player in the industry, with a 32 per cent market share, behind Auto Glass, which has about 36 per cent of the market. The acquisition will operate as RAC Auto Windscreens and it has entered into a service contract with Lex. Some 53,000 car windscreen replacements or repairs are currently referred by Lex companies to other suppliers. This business will now go to RAC Auto Windscreens. The visibility of the RAC brand will also be raised, as it will be put 772 Auto Windscreens vans. Lex shares closed up 24p to 482.5p.