The absence of a permanent CEO has been a major concern cited by investors seeking a clear strategy from the company after months of financial pressure, weak platinum prices and a wave of deadly strikes at South African mines.
Chief Financial Officer Simon Scott had ruled himself out of the job on a permanent basis, Lonmin said, but he would continue to fill the role until a replacement was found.
Farmer was admitted to hospital in August, coinciding with a wave of unrest at the group's Marikana mine that left 46 people dead and paralyzed operations.
The strikes increased pressure on a company that was already being squeezed by high costs and weak platinum prices.
It was forced to turn to investors last month to raise $817 million to avoid breaching lending terms.
Its biggest shareholder, miner Xstrata (XTA.L), which holds a 25 percent stake, supported the rights issue but it said it wanted management changes.
Lonmin chairman Roger Phillimore said the group would miss Farmer's ability, commitment and drive at the company, where he worked for more than 26 years, including four as chief executive.
Shares in Lonmin were trading down 1.79 percent at 280.4 pence by 5.44 a.m. ET, underperforming a flat mid cap index .FTMC in London.
The stock has gained some ground since November 9, when it touched a 13-year low of 227 pence, but it remains 45 percent down on its level 12 months ago.
(Reporting by Paul Sandle; Editing by Helen Massy-Beresford and Hans-Juergen Peters)
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