While Klaviyo doesn't have a built-in integration with Leadpages, it's possible to sync a Klaviyo signup page through an HTML widget in Leadpages.
Connect a Klaviyo Sign Up Form to Leadpages
Follow the instructions here for adding an HTML Widget using the Drag and Drop Builder in Leadpages (available with the new user interface in Leadpages only). In Leadpages you will see the following for entering HTML code.
In Klaviyo, go to the Lists and Segments tab and click through the list you would like to connect to Leadpages. Then navigate to Signup Forms > Condensed Embed.
We recommend using Condensed Embed code only.
Copy all the code provided and paste this code into the HTML widget in Leadpages pictured above and click to save. Follow the instructions in Leadpages to make the signup widget live and test with a new email address to ensure signups will flow into Klaviyo.