“Lives” is the plural of life. “People” is a plural noun we then say “people's lives”. We talk of other areas of people's lives and older people's lives, young people's lives We can discuss people's lives beyond their workplaces. People’s lives are documented in biographies Do not compare your life with other people’s lives

Both 'people's lives' and 'people's life' are correct, but they are used in different contexts. 'People's lives' is the plural form and is used when referring to the lives of multiple individuals. 'People's life' is the singular form and is used when referring to the collective life of a group of people.