Ricky Sbragia's situation at Bolton Wanderers is causing dressing room unrest.
The Scot is rated highly by senior figures within the team and he was a key man under Allardyce.
But after promoting Gary Speed to a player-coach role in the summer and appointing former Everton No 2 Archie Knox as his right-hand man last month, Lee has pushed Sbragia down the pecking order.
Lee, who could face the sack if bottom club Bolton lose at home to Spurs today, insists he is keeping Sbragia involved by allowing him to do pre-match warm-ups at the club.
Lee said: "We've got this structure now where Jimmy Phillips will travel away to do warm-ups and Ricky will do it at home.
"We don't want to be overloaded with people when we travel away."