The 20-year-old striker was on target against Lusitanos away from home in Andorra on Thursday.
The youngster’s goal in the 21st minute proved to be the difference between the two sides, as West Ham won the second leg of the Europa League first qualifying round 1-0.
The Hammers have now progressed to the second qualifying round of the prestigious European competition 4-0 on aggregate, having won the first leg of the tie 3-0 at the Boleyn Ground last week.
Former Southampton, Blackburn and Newcastle striker Shearer was impressed with Lee’s first senior goal for West Ham and has backed him to score more.
Lee made just one appearance for West Ham in the Premier League last season.
It came against Newcastle away from home at St. James’ Park on the final day of the campaign.
Lee came on for the final 14 minutes and gave a decent account of himself during the Magpies’ 2-0 defeat.
The youngster had a pass accuracy of 50%, and won one header, one dribble and one tackle.