Currently, there is no option to export lists out of NXT web view. 

Alternative Solutions:

Share the lists with others
1.  Open your list
2.  Copy the full URL of the list (appears in the address bar of your browser)
3.  Send the URL to the user you wish to access

*Note* To have another user view your list be sure to grant rights for others to view or edit.

OR

Save your list to the database view

1.  In the web view list, click save
2.  Choose to save to the database view as a static query
3.  Open the query in the database view and export the static query
4.  Or take the query into the Export module and then export the list
*Note* Not every Output field/Column in the NXT web view for the List is available in the database view under Query and/or Export.