I see it from a different perspective: To make that vision of future self come true, present self must instigate the changes necessary, one of which may be letting go of the past. The comic presenting these as lives I think makes it more definitive and yet helps you to detach from it somewhat. Consider it like this: a very close friend wants to become a carer, for the elderly or disabled; what would you as a person do to facilitate that? What actions must they take that you can directly help or influence? You have a few years to help this person so try and answer this for both the short and long term. Would you be willing or able to give up personal time to help them? What would happen if you didn't? If your friend needs to quit a bad habit, would you take the same steps as them to help support them?
The "friend" is your future self, your present self can choose to help your future self or not; to put it into a common frame of reference, if you'd help your friend to achieve something, what's stopping you from helping your future self do the same? The comic doesn't directly reference this, just simply saying "These are your lifetimes. USE THEM." so all of this is just my interpretation of it, but it seems logical to me that once you start thinking about your life as a series of lives (or different selves) you can plan accordingly. Feel free to disagree, if you interpret it differently then I would love to hear your perspective. :)