Lee tied it 1-1 at 10:03 of the second period, redirecting a point shot from Pelech with one hand on his stick while battling Marc-Edouard Vlasic for position in front.
Parise put the Islanders in front 2-1 at 14:48 when Dobson's shot redirected in off his left skate.
"He's a guy who's always around the net," Lambert said. "He got rewarded for it."
Svechnikov tied it 2-2 at 17:10 with a similar goal to Parise. Following a turnover by the Islanders while trying to clear the puck, Matt Benning's initial shot was saved by Varlamov, but the rebound deflected in off Svechnikov's left skate.
"We have to play more aggressive," Sturm said. "Let's face it, we're not going to blow out teams out there. [We're not] going to score five, six goals every game, so we have to figure out how we start winning games when you score two or three goals."