Per default only pages of the post type "Page" are showing in the dropdown. If your template page is from a custom post type, it won't show in the dropdown per default.
For custom post type templates to appear in the dropdown, you will need to select the custom post type in the "Settings" tab inside LPagery.
How to Enable Custom Post Type Support
Go to "Settings"
Enter the name of your custom post type and select it from the results.
Return to the "Create Pages"
Your template page should now appear.