Sunderland were beaten 3-1 by Arsenal at the weekend.
Lens was handed a rare start for the Black Cats in their FA Cup fixture at the Emirates Stadium on Saturday, and he managed to get on the scoresheet in the contest.
Lens opened the scoring in London, but he was unable to stop his side falling to a 3-1 defeat.
His performance was one which still earned him credit from Allardyce however, with the 61-year-old boss now hoping the Dutchman can play a big role in his side's season.
“He’s one of the most expensive players we’ve bought in recent years, so you’ve got to ask that player to live up to that reputation. Some of the skills and ability he showed on Saturday were very encouraging – he scored and looked very strong," Allardyce said.
“Certainly, Saturday’s performance was very encouraging in the hope that he can continue to perform to that level, if not better.”
Lens has found first team chances hard to come by ever since Allardyce took charge.
The 28-year-old has generally been deployed as a late substitute since Allardyce was appointed as boss, and he spoke of his frustrations about his time at the Stadium of Light last month.
Lens seemed to suggest that a move was possible in January, but Allardyce says that he has received no offers for the wide man.
“We haven’t had any interest in Jeremain from anybody else, so I would want him to be a big part of what we’re trying to do to get out of the trouble we’re in,” the former West Ham United boss added.
Lens has scored three goals in his 16 Sunderland appearances to date.