Investigators are seeking a motive in the shooting of a woman found lying on the sidewalk in front of her home. Police said yesterday that the 29-year-old woman had suffered what appeared to be a single gunshot wound to the lower back late Wednesday. She was taken to a hospital outside the city and is expected to survive. Officers later arrested Sann Than, also 29, who shared the Gold Street address with the victim. Investigators also recovered a 9mm semiautomatic handgun whose serial number had been wiped out. The man was arraigned yesterday on firearm violations, assault and battery with a dangerous weapon, and other charges. Than was ordered held on a $25,000 bail in the shooting, and bail was revoked on previous illegal firearm possession charges. He is due back in Lowell District Court on Aug. 15.