The source said the two killed were a 70-year-old man and a 38-year-old man, both from the Sunni Muslim neighbourhood of Bab el-Tebanneh.
At least 27 others were injured in the clashes, including three who were in serious condition, the source said.
The Lebanese army has been deployed in the area but fighting was ongoing in the town, where clashes have frequently broken out since the beginning of the conflict in neighbouring Syria in March 2011.
Clashes have often pitted residents of the Sunni district of Bab el-Tebbaneh against those from the neighbouring Alawite district of Jabal Mohsen.
The latest round of violence began on Sunday, as the Assad regime began an assault on the rebel stronghold of Qusayr, and has left at least four people dead, including a soldier.