This is possible by using Edit Draft on your Landing Page template. You can update your Template style by editing the HTML. When you do this, however, be sure that the Classes and IDs of your mktEditable sections remain the same to ensure that content you've added to your child LPs is safe. Once you're happy with your updates, you can approve your template draft and this will create a draft of all of the LPs using this template. You can then approve them en masse from Design Studio > Landing Pages.
You can clone a landing page and then select a new template, however I have run into issues where the layout doesn't always adhere to how you had it on the template prior. So I would clone it, go in and adjust the elements so they look the way you want them to, and then approve the landing page. If you are replacing the old LP entirely then you will also need to change the old LP's URL, so you can replace the new LP's URL with the old one.