Comparison Operators not working for conditional author post thumbnails

You are using wrong Comparison Operators.

Use

else if($author_id == "2") {

instead of

else if($author_id = "2") {

Edit: Try adding trailing slash after get_stylesheet_directory_uri function. its missing in your code.

<img src="https://wordpress.stackexchange.com/questions/166850/<?php echo get_stylesheet_directory_uri() ?>/images/default-thumb.jpg" alt="" title="" width="" height="" />