"He is doing light training now and that will be stepped up to full training," says Paul Goddard.
"He feels better with it and it is something that probably needs a bit more rest to get rid of it totally - but it is not a major problem.
"Hopefully what he has had done will be an improvement and he will be able to kick on a bit more."
Lee has had a niggling problem with the ankle since coming to West Ham, but, typically, played without complaining or seeking a rest.
And it is that sort of unswerving spirit and desire that will be much needed at the weekend, says Paul, as the Hammers go into the first of a trio of 'six pointers' before the end of the season against the other bottom four clubs.
The Hammers have recorded a loss, a draw and a win thus far against Sunday's opponents, Bolton, and Sunderland respectively, with this weekend seeing a chance to avenge that 1-0 home reverse in September.
"West Brom fans are very passionate and they have not been in the Premiership for a long time; they don't want to go back out and they will be urging their team on," says Paul.
"It will be a very hot atmosphere on Sunday and we have to make sure we are ready for the challenge, play the game in the right manner by competing and also trying to play our football when we can.
"You have got to compete from the start in any game - and if you do not match people for competitiveness you are going to be in trouble.
"It is vital, something we have got to do from the word go."