The 18-year-old will remain with the U's until after their clash with Preston on November 23.
He is expected to be involved on Tuesday night as Joe Dunne's men face Shrewsbury in Sky Bet League One.
Lee has scored five times in six games for the Hammers' under-21 side this campaign and made his Barclays Premier League bow as a substitute during the club's defeat to Stoke in August.
The Durham-born forward made his first-team debut in last season's FA Cup third-round replay defeat to Manchester United.
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- Joe Dunne
- Barclays Premier League