This follows an appeal for information about two men three days ago regarding the same incident, which took place at 2pm on Tuesday, August 3, at the store in Burgh Road.
In the latest statement, Lincolnshire Police say a man walked into the store and selected a bottle of Gin to the value of £30 and two bottles of soft drink.
He then attempted to leave without paying and when he was challenged, he made off.
The man is described as being approximately six foot tall and is believed to have been wearing a navy jumper, black jeans and a grey hat.
The second man has since been identified.
"We believe the man pictured can help us progress our investigation," said the statement.
Anyone who can identity of the man in the photograph or have any other information, is asked to call 101, quoting incident number 21000434902.
Alternatively email PC Paul Harvey at [email protected], quoting the incident number in the subject box.
You can also remain anonymous, by reporting via the independent charity CrimeStoppers on 0800 555 111.