According to police, officers responded to 1082 E. 105th Street for shots fired at approximately 5:40 p.m. on Thursday.
The 27-year-old man was shot in the chest in the lot, walked to E. 105th Street and Ostend Avenue and collapsed, police said.
Police said officers on scene learned the victim was either walking or standing in the lot when he was shot by an unknown man.
A 40-year-old woman was driving into the lot at the time when a bullet struck her car, according police.
The woman reportedly suffered a minor abrasion to her face.
Cleveland Police said she was not involved with the first victim or the suspect.
Police described the suspect as a man in his late 20s, 6 feet tall with a slim build.
No arrests have been made as this investigation continues.