The Poland striker opened his account in the first leg against Real Madrid in the eighth minute and added three more in a stellar second half to give his team a 4-1 advantage to take into Tuesday's return leg.
Lewandowski, who has scored in his last 12 league games, took his tally to 21 goals in 19 matches and sharpened the interest of major European clubs eager to sign him.
He has refused to sign a contract extension beyond 2014 but has kept quiet about his plans and Dortmund officials remain optimistic of keeping him.
"Robert has a contract until 2014 and there is no exit clause like with Mario Goetze," said club boss Hans-Joachim Watzke. "It is our explicit wish to keep him until 2014. That is why we are saying no to a transfer fee."
Dortmund have already lost one of their key players, Mario Goetze, with Bayern Munich paying £32million for the gifted 20-year-old Germany international.
Speculation has been swirling around central defender Mats Hummels with media reports linking him to a move to Spain.
"This (performance) will definitely go down in history. There are always the same films in the Borusseum. You will see Lewa's four goals there soon," said coach Juergen Klopp.
"It was an unusual game by my team and that third goal was worth every cent the broadcasters paid.
"I do not have the feeling that Robert is on the run and we are not the ones to send him away," he said. "Let's wait and see what happens next."