Moyes has come in at the London Stadium, but only on a contract until the end of the season.
And Lee feels that the short-term nature of Moyes’ deal proves that West Ham’s owners won’t be backing him with funds in the January transfer window.
“I actually think he’ll do well,” Lee said.
“They’re obviously not going to give him any money at all in January, because they’re giving him a six month contract. He’ll have to work with the players he’s got.”
Moyes has a tough job on his hands at the London Stadium, as there are serious doubts over his appointment.
The large majority of West Ham fans have not reacted well to Moyes coming in, and even co-owner David Gold has admitted that he has taken a gamble.
West Ham are currently in 18th place in the Premier League standings, after what has been an awful campaign so far.
Moyes’ first game in charge at West Ham comes in two weekends’ time, when the Hammers go to Vicarage Road to take on Watford.