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.