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.
1. An electricity substation shows the signs of damage the morning after a rocket strike the previous evening
Aseries of rocket strikes hit targets across Lviv, with columns of smoke filling the sky over the city. Photo by Leon Neal/Getty Images Photo: Leon Neal
2. Fire and smoke are seen following explosions after a Russian missile strike on May 3, 2022 in Lviv, Ukraine.
Lviv Mayor Andriy Sadovyi said on the social media service Telegram that multiple power substations had been damaged by missile strikes, injuring at least two people, and some parts of the city are experiencing power outages. (Photo by Leon Neal/Getty Images) Photo: Leon Neal
3. Smoke rises after a Russian missile strike in Lviv, Ukraine, late Tuesday, May 3, 2022.
Russian missile strikes targeted the city in western Ukraine on Tuesday, hitting electrical substations and disrupting power. (AP Photo/Jon Gambrell) Photo: Jon Gambrell
4. An electricity substation shows the signs of damage the morning after a rocket strike the previous evening, on May 04, 2022 in Lviv, Ukraine.
An electricity substation shows the signs of damage the morning after a rocket strike the previous evening, on May 04, 2022 in Lviv, Ukraine. Photo by Leon Neal/Getty Images Photo: Leon Neal