Europe trail the US 10-6 heading into Sunday's singles matches at Medinah, the final day of the competition.
"There's still 12 singles matches tomorrow," said Lawrie on Saturday. "We can all win tomorrow and why not?
"It's certainly not over. It would be nice to make a big comeback tomorrow, so we'll see what happens.
"It's always possible. Until it's impossible to do it, then you fight on, certainly for Jose Maria [Olazabal] this week. No one is going to be giving up."
Europe need to score eight points from the 12 singles to reach 14 points and retain the Ryder Cup, while the US need four and-a-half points to win the competition.