Under the terms of yesterday's deal, Lex Service is paying pounds 83.5m for an additional 30 per cent stake, with an option to buy the remainder in three years.
The deal follows a statement by Arriva, the former Cowie bus group, that it has received expressions of interest in its vehicle-leasing division.
The Lex deal arose because Lombard is keen to concentrate on its own contract-hire business, British Car Contracts.
The deal was announced as Lex Service reported a strong set of interim results, with half-year profits up by 18 per cent to pounds 36m and good performances across the group in leasing, trucks, car parts and the Hyundai dealerships.
The results were in stark contrast to other companies in the sector, such as Car Group, the second-hand car dealer, whose shares have been devastated by profits warnings over tumbling used car prices.
Lex said the downturn in prices had affected disposal profits, and this was expected to continue in the second half.
The interim dividend was increased to 7.8p up from 6.8p last year. The shares closed 17p higher at 511.5p.