How to use leanModal for loading a node or content in Drupal 7? I'm using this http://leanmodal.finelysliced.com.au , but unable to achieve the goal since I need that after clicking on my button the new content or a url for an instance node/3 should get load in this modal, any idea how can I do it?
The leanmodal javascript plugin specifically states that it does not include AJAX support. That means that whatever content you want to appear in your modal needs to be already included on the page content when the page initially loads.

If you want to load a different page's content in the modal, then you will need to use an approach that includes AJAX support. I would recommend one of the many Drupal options that provide this sort of functionality, such as Simple Dialog or cTools Auto-Modal. 

The exact implementation will depend on the specifics of what content you are trying to load and in what context.