Gearset is fully Lightning ready, and allows you to easily move your Lightning components and pages between your orgs.
In my org below, I've created a simple one-column Lightning page with some text.
In the results of my comparison with Gearset, this now appears as a Lightning page item in the results. Selecting it shows the XML for the page, where I can see my example text and other configuration settings.
Deploying this page is the same as any other metadata deployment with Gearset. Simply select the checkbox next to its name, click "Next", and then "Deploy now". Once the deployment completes, the Lightning page will be available in my target org.
Note: Gearset's default metadata filter includes Lightning pages but not Lightning components. To view and deploy your Lightning components, you'll need to add them into a custom metadata filter. You can see how in this article.