How to tell this other way? Can it be said

How to tell this other way? Can it be said like this: They have been active all their lives?

Yes, that is perfectly acceptable and conveys the same meaning.

Another common variation of the original phrasing is “They have always led an active life”.

It is a very common idiom “to lead” a certain kind of life.

They lead an active life.
I lead a sedentary life.
She leads an interesting life.

This is an irregular verb: Lead / Led / Led

It can mean to conduct: lead an active life, lead the orchestra
It can mean to give direction to: lead a parade, lead an army

A well-known adage: You can lead a horse to water, but you can’t make him drink.
I like how that is sometimes paraphrased: You can lead a student to knowledge, but you can’t make him think.