Musselwhite, 41, will be in the dugout at Southend United on Saturday as the Imps begin life after Chris Sutton.
The former Celtic forward, who was appointed as manager in September 2009, cited personal reasons for his surprise resignation on Wednesday.
Musselwhite made 245 appearances in two spells for the Iron, and had been goalkeeper coach at Sincil Bank.
Bob Dorrian, the Lincoln City chairman, suggested Lindsey and Musselwhite were not in the frame to replace Sutton on a permanent basis at the League Two club.
The appointment of Sutton last year came after a long search, but Dorrian said that was largely because the caretaker coach then Simon Clark was more experienced.
"They [Lindsey and Musselwhite] will take charge of the game on saturday at Southend and any ensuing games," he said.
"Last year we had Clark, who was very capable, looking after the side who was very capable. This time it is very different with Scott and Paul who are very inexperienced, so we will look at moving a bit quicker.
"I suspect that we'll probably be looking again at somebody up and coming, maybe from the non-leagues. Or alternatively a young, experienced league manager or ex-league manager."
Musselwhite is one of two former Iron players currently assisting caretaker managers at a lower league club - Steve Torpey is supporting Andy Porter at the Blue Square Premier side York CIty.