Lee was initially named assistant under Sam Allardyce in January before taking up the same role during Frank de Boer's brief tenure at Selhurst Park.
The Dutchman was sacked after just 77 days in charge at Palace and replaced by former England boss Hodgson on Tuesday.
Lee, who has had two spells working on England's coaching staff, has been replaced by Ray Lewington.
Orlando Trustfull, brought in by De Boer also as an assistant manager, and Ryland Morgans, who was head of performance, have also left the Premier League strugglers.
A statement on the club's website read: "We would like to thank Orlando, Sammy and Ryland for their efforts during their time in south London, and wish them all the very best for the future."