The surprise departure of Mr Rice, whose windfall will total pounds 17m after proceeds of pounds 13m-worth of share options, comes amid rumours of a personality clash with Joe Gorman, TRW's forceful chief executive.
Mr Rice was expected to become vice-chairman of the enlarged group and the head of its automotive division, following January's cash bid by TRW.
However, in a last-minute U-turn, Mr Gorman is believed to have withdrawn the offer, asking Mr Rice to remain simply as a board member and a part- time consultant.
The Lucas chief executive has still not replied to Mr Gorman's proposal. But even if he accepts a reduced role, Mr Rice will still receive a pounds 4m- plus compensation package agreed in 1996 when Lucas merged with Varity.
Lucas and TRW declined to comment yesterday but industry observers said that Mr Gorman's decision is a huge blow for Mr Rice.
During the takeover negotiations, he defended the TRW offer against a competing bid from Federal Mogul and repeatedly said that he wanted to play a major part in the enlarged group.
The boardroom shake-up came after Lucas became embroiled in a row with the unions after putting its car wiring division up for sale.
The AEEU engineering union said the sale of the business, which employs 4,000 people in the UK, could see the closure of a plant in Houghton- le-Spring, Sunderland, with the loss of 700 jobs. Ken Jackson, the AEEU general secretary, said that he would ask the company to guarantee the future of the factory at a meeting next week.
Meanwhile, it emerged yesterday that Paul Brett, the chief executive of Thomson Travel, received a pounds 3.2m one-off payment from the publishing group Thomson Corporation, the holiday group's former owner, following last year's flotation. The chief operating officer Roger Burnell got a pounds 1.45m windfall.
In another development, Rana Talwar, the chief executive of Standard Chartered, the financial house, received a 28 per cent pay rise last year to pounds 1.09m.