Two menus (float one right, float one left)

Simple question: I would like to have two horizontal menus in the header of my site. I’d like to float one left and the other right. The menus should have different information.

(i.e. Right menu: Home, about, clients –> Left Menu: Pricing, Blog, Contact)

Would I need to create a new header.php file (one file for the left menu, one file for the right menu)? Or is there a simple workaround.

The menus are unordered lists. The site is currently hosted here: childtheme.alexluprete.com

Thanks for the help. I am still a bit new to wordpress and programming.