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I'm with Michael on this one.
Changing lives matter.
This sentence means something like "people who are changing are important."
In this sentence, "changing" is an adjective, and the verb agrees with the noun "lives."
Changing lives matters.
This sentence means something like "making a change to people's lives is important."
In this sentence "changing" is a gerund, and "lives" is the object of the gerund; therefore, the verb agrees with "changing."