How do I determine the "hand" of the door?
The handle pictures in the second diagram is very misleading.  Since the outside handle is obvious, the second pic should be the inside picture, but thet are labeled wrong for this handle it appears.  My guess is that the second pic is meant for any interior door, and for exterior doors with special exterior handles, it is wrong.

You are right, your door is left handed.  I think you would be safe ordering the LH handles.  If you are still nervous, I would take a trip to home depot or lowes to look at similar handles and confirm that LH is the way to go.

Here is the link to the actual product on the Schlage website.  Unfortunately, I dont see much to help even in the documentation.  I do see that you can flip the handle if desired, but then the curvature would be up and not down on the handle.

Also FYI, most interior door handes are reversible.  But in your case, since it is an exterior handle, it does matter.