The Lions lost 45-10 to the Kansas City Chiefs at Wembley Stadium on Sunday to leave them with one win and seven losses from their first eight games this campaign.
Lewand was in his 20th season with the franchise while Mayhew had been the team's GM since 2008, but after the club reshuffled their coaching staff at the end of last month, they have now made further changes to their backroom in a bid to turn their season around.
Mayhew told reporters last week that he had made mistakes in drafting players for this season after several first-round picks failed to emerge as successes at the franchise.
"I've got to do a better job drafting across the board in general," The Guardian quotes him as saying. "And by no means do I mean that I have been outstanding in terms of our draft.
"We have drafted some really good players and we have missed on some players. I think that if you look around the league, that is pretty common. But we want to be perfect. We want to be perfect."
The Lions have a bye this week, with their next game coming against the Green Bay Packers on November 15.