I can't find a way to make an alternate for this page, what would be the best way to add css classes to the elements on this page? 

Why do you need an alternate? Or do you mean a template override in your theme?

Yes, I mean a template override. 

What did you try so far? Did you try to simply have a Logon.cshtml file in the views folder of your theme?

Well, I have a LogOn-url-users.cshtml file but that doesn't seem to include the form for the lost password page.

1. Copy  RequestLostPassword.cshtml to ~/themes/<YOUR THEME>/views/Orchard.Users/Account/RequestLostPassword.cshtml

2. Modify this copy as necessary

Awesome, thanks.