Is money earned from selling designs or permissible services through foreign websites, which display Google AdSense advertisements and pictures of unveiled women, considered lawful or unlawful?

The fact that websites may display prohibited advertisements does not prevent dealing with them in permissible matters, provided that their work is not exclusively, or predominantly, involved with the prohibited. If this is their situation, and your work with them involves designing things that do not violate Islamic law, whether it's promoting your work for a commission or your design work for a commission, then both matters are permissible.