After I Install this setup file in here http://system.data.sqlite.org/index.html/doc/trunk/www/downloads.wiki which is an ADO.net provider for SQLite with exactly following the instructions here: https://stackoverflow.com/a/39322959/9131071 with Install the designer components for Visual Studio 2015 option being checked.
When I reinstall the same without the above option being checked - I could see the option listed there.
Now, what is the solution to get this.. since I need both an ADO.net provider and the option on the list?