The Co-operative said James Mack, 41, its chief financial officer was leaving to take up another job in the industry. The £750 million deal was agreed last July, but the Co-op has been under regulatory pressure over its senior management team.
Lloyds has a November deadline set by European regulators to sell the branches, 182 of which are in Scotland.
Charlotte Sjoberg, spokeswoman for the bank's Project Verde, said: "The position remains exactly the same, we are on track with the Co-op and that is what both parties are working towards."
But one City analyst said Mr Mack's departure throws fresh doubt on the deal. "This takes the chances of a sale down to 50-50," said Christopher Wheeler at Mediobanca.
"Lloyds will be brushing off their IPO possibility, though the worry is that RBS has dusted off the IPO possibility for the sale of its branches too."
RBS has to sell its 316 branches after a sale to Santander collapsed in November.