Chris Wright, who joined Lasmo in July 1997 from Burmah Oil, is in line for a pounds 600,000 pay off. He was on a two-year contract and was paid pounds 280,000 in 1998.
A spokesman insisted that there had been no dispute between Mr Wright and Mr Darby over the strategic direction of Lasmo.
"He and Joe had different management styles. It was a clash of personalities," he said.
Along with Mr Darby and Paul Murray, Lasmo's finance director, Mr Wright was one of a key three-man team steering the business.
He was closely involved in the decision by Lasmo not to merge with the rival exploration group Enterprise earlier this year.
His departure took even Lasmo insiders by surprise, fuelling suspicions that it may have been prompted by more than just a personality clash. Lasmo is in the middle of a strategic review which has involved a great deal of contact between its three executive board directors.
Mr Wright is not being replaced directly on the board. Instead three Lasmo executives, Roger Tucker, president of its Venezuela operations, Peter Wells, managing director for the Middle East, and David Thomas, who is in charge of Europe and North Africa, will assume wider responsibilities and report directly to Mr Darby.
Lasmo is undergoing a rationalisation which has reduced the headcount by a third and more than halved the workforce at its London headquarters.