The 22-year-old enjoyed a fruitful loan spell with the Hatters from West Ham during the 2014-15 season, scoring with virtually his first touch when coming off the bench against AFC Wimbledon in February.
He netted a double against Wycombe too, before being injured in the same match that hindered the rest of his time at Kenilworth Road.
Lee went back to the Hammers and had spells at Blackpool and Colchester the following the season after, before leaving the Hammers in the summer of 2016, signing for Barnsley.
He has struggled to break in at Oakwell though, restricted to just six substitute appearances for the Tykes last term, his fine one coming in the 3-0 defeat at Newcastle on the final day of the campaign.
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However, speculation has been rife he will make a return to Luton, where he would link up with brother Olly.
The Hatters are in the market for a striker after Jack Marriott joined Peterborough last week, leaving them with Danny Hylton, Isaac Vassell and recent addition James Collins.
The relatonship between Luton and the Tykes is good too, with midfielder Cameron McGeehan recently making the switch to Oakwell for an undisclosed fee.
Lee’s arrival would made it six new additions for the Hatters with Alan McCormack, Marek Stech, Jack Stacey, Collins and Andrew Shinnie all putting pen to paper so far.