"Hopefully he's got to grips with this level of football, which is hugely difficult in your first season in the Premier League," Allardyce told British media.
Media reports had speculated Allardyce might want to sell Lens, particularly after dropping him and fining him two weeks' wages for refusing to take part in a post-match workout last month.
But the manager said he wanted the forward to help Sunderland, currently second from bottom and four points adrift of safety, survive in Premier League instead.
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"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 manager said.
"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."
Sunderland travel to Swansea for their next Premier League match on Wednesday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
