Neighbouring country Moldova also reported "massive" blackouts, although it has not been directly hit.
Lviv's mayor urged people to take shelter, while the head of the wider Kyiv region said critical infrastructure and homes had been hit.
Russia has recently increased its attacks on Ukrainian energy networks.
Earlier, an air-raid alert was issued across Ukraine amid reports of explosions in a number of locations.
The Lviv mayor, Andriy Sadovy, said children had been taken to shelters with their teachers - and urged parents not to pick them up until the alarm was over.
Shortly before the fresh reports from Kyiv and Lviv, officials said southern Ukraine had come under renewed assault.
The governor of the Mykolaiv region warned of "many rockets" arriving from the south and east.
In the nearby Zaporizhzhia region, a newborn baby was killed when a missile hit a maternity unit, emergency services said.
Russia was blamed for that attack, but is yet to comment on any of Wednesday's alleged strikes.
Scheduled and unscheduled blackouts have become common in many parts of Ukraine as a result of the recent attacks.
Russian attacks have damaged almost half of Ukraine's energy system, and millions of people are without power as temperatures drop for winter.
In recent days, the head of Ukraine's biggest private energy firm said people should consider leaving the country to reduce demand on the country's power network.