The phrase "make our lives better" is correct and usable in written English.
You can use it in many contexts. For example, "Our new slogan is 'Let's work together to make our lives better.'".
"Beautiful words cannot make our lives better.
Beautiful words will not make our lives better.
"It's about creating the tools that make our lives better," he said.
"Not just 'Is it cool?' but 'Does it make our lives better, or more just?
They're the ones who make our lives better despite the occasional slip of the halo.
"Technology was supposed to make our lives better," the narrator gravely intones.
"They show that solidarity and offering a hospitable welcome really do make our lives better".
They make our lives better, just as art does, and theatre, and music.
"We do not see who or what company could make our lives better," she said.
Data, data everywhere – but will it make our lives better, or put us at risk?
We will vote for people who make our lives better," said Kaleem.
