Jurgen Klopp's side are the only unbeaten side in England's top five divisions with 14 wins and three draws and their Croatia centre-back thinks they could match the achievement of Arsene Wenger's Gunners in 2003-04.
"Hopefully we can be unbeaten until the end of the season," said Lovren, buoyed by Sunday's victory over arch-rivals Manchester United.
"Of course it will be a challenge but this is what we want, this is why we came here to Liverpool, because we know we can do it. Arsenal did it before so why not?"
Liverpool have not won a top-flight championship since 1990 but appear to be best-placed in all departments to make a bid to end that run.
They could extend their lead over defending champions Manchester City to four points with a win at Wolves on Friday to add an extra bit of pressure for Pep Guardiola's chasers.
However, Lovren knows their title rivals have few weaknesses and the outcome of the season will most likely come down to who makes the fewest mistakes.
"I'm not sure that they have any weaknesses," he added. "Last year they won by 19 points. They know how to manage even when they lose. They also lost one or two games last year and still they managed to be 19 points ahead.
"It doesn't mean anything. There are so many games in front of us and in front of them. It will be a tight race and it's not only City, Tottenham are only a few points behind."