Bo Horvat scored, and Jaroslav Halak made 34 saves for the Canucks (15-15-3), who were coming off a 2-1 overtime win at the Anaheim Ducks on Wednesday.
"Just didn't find our legs for a while there, but we fought back in the third and got a point out of it," Vancouver forward Conor Garland said.
Lemieux gave Los Angeles a 1-0 lead at 7:39 of the second period. After an aggressive forecheck by Blake Lizotte forced Canucks defenseman Luke Schenn into a turnover, Christian Wolanin got the puck at the left point for a shot that was redirected in by Lemieux.
"I know 'Lizzo' and I try to make that a staple of our game, being a really aggressive forechecking line," Lemieux said. "Spending time in the D-zone, making it really hard for them to break out, so that we can create offense but also so that we can create momentum for the next line and hand off a good shift. And I think we did a pretty good job of that. … From top to bottom, I think every line had their shifts and their pressure, and that's why that game seemed where we had them on their heels for most of it."
Lemieux had the chance to extend the lead 57 seconds into the third period, but his attempt five-hole on his first NHL penalty shot was saved by Halak.
"It was a long shift, and to get it then … yeah, wasn't my best," Lemieux said.
Horvat tied it 1-1 at 12:06 of the third. He redirected in a backdoor pass from a diving J.T. Miller on the power play.
"I was just trying to find open ice and get to the net when I saw J.T.," Horvat said. "Obviously, it was good to get that one and good to get a point, but we've got to be better in the future."