"Something made our lives easier" is correct. "Lives" is the plural form of "life".

It's the same as knife and wife - the plural forms are knives and wives. In fact, many nouns ending in 'f' change to 'ves' in the plural - loaf/loaves, shelf/shelves.

you would use 'our lives' when talking in the plural ('We'), and 'my life' in the singular ('I').