The two countries have so far disagreed over how to handle the conflict, with Russia teaming up with China at the UN Security Council to water down any motions about Syria.
Baird will ask Lavrov to help continue to work toward a political solution in Syria, the CBC's Hannah Thibedeau reported Thursday.
Baird downplayed hope that a solution could come out of the G20 meeting where world leaders have gathered.
"We've got to be very realistic. No one is coming here anticipating success. This is fundamentally an economic forum. I think this is the first time that any number of foreign ministers have gathered here," he said to reporters on Thursday.
"Obviously when you have this type of crisis... there's no doubt that it casts a shadow. I think what we hope to have is a good dialogue on these issues.
"Certainly I and the prime minister were very realistic that at this forum we weren't likely to come to a conclusion."
Baird calls on UN to report on chemical weapons
Baird says the only way to end the suffering for Syrians is a political solution, though he was clear that he believes the regime of Bashar al-Assad was behind a recent chemical weapons attack on civilians. He also called for the UN to finish its investigation into the attack and report quickly on the results.
"I understand where people are coming from in the West and the concerns about what happened with Iraq," he said, referring to false reports that former Iraqi dictator Saddam Hussein had weapons of mass destruction.
"I think this intervention that the U.S. and others [are] contemplating, some 30 months into this war... [President Obama has] been very reluctant to intervene militarily and I think that's self-evident."
"Obviously the evidence for the world is conclusive is that these weapons were used. The signatures of the delivery of these mechanisms is what Assad holds. And obviously I think there is requirement for an appropriate response," Baird said.