A desperate flight to a better life at Lviv’s train station.

LVIV, Ukraine — Older men and women and young mothers clutching their children’s hands gingerly made their way down the steep steps of a blue train car on Wednesday afternoon.

Some had been onboard the train for more than 20 hours, traveling from cities and towns near the front line of the war in the east to the relative safety of Lviv, the largest city in western Ukraine, which has been a refuge for thousands of people fleeing strife elsewhere in the country.

The desire to flee has become…