The strikes damaged three power substations, knocking out electricity in parts of the city and disrupting the water supply, and wounded two people, the mayor said.
Lviv has been a gateway for Nato-supplied weapons and a haven for those fleeing the fighting in the east.
Russian Defence Ministry spokesman Major General Igor Konashenkov said Russian aircraft and artillery hit hundreds of targets in the past day, including troop strongholds, command posts, artillery positions, fuel and ammunition depots and radar equipment.
Ukrainian authorities said the Russians also attacked at least a half a dozen railway stations around the country.
5. Dark smoke rises following an air strike in the western Ukrainian city of Lviv, on May 3, 2022.
Dark smoke rises following an air strike in the western Ukrainian city of Lviv, on May 3, 2022. (Photo by Yuriy Dyachyshyn / AFP) (Photo by YURIY DYACHYSHYN/AFP via Getty Images) Photo: YURIY DYACHYSHYN
6. A large piece of missile fragment is seen outside an electricity substation
A large piece of missile fragment is seen outside an electricity substation the morning after a rocket strike, on May 04, 2022 in Lviv, Ukraine. Photo by Leon Neal/Getty Images Photo: Leon Neal
7. Fire and smoke are seen following explosions after a Russian missile strike on May 3, 2022 in Lviv,
Russian Defence Ministry spokesman Major General Igor Konashenkov said Russian aircraft and artillery hit hundreds of targets in the past day Photo by Leon Neal/Getty Images Photo: Leon Neal
8. A street cleaner sweeps the pavement outside an electricity substation
A street cleaner sweeps the pavement outside an electricity substation Photo by Leon Neal/Getty Images Photo: Leon Neal