From what I've seen, it seems the red was rather thinned down. When applied to the standard Fokker streaked finish, some of the darker streaking sort of showed through and made the red look darker. Over the areas of the national markings where there was a white background, the red was lighter due to the white affecting the red color.
FYI: Meteor Productions just released two 1/32 scale decal sheets for the Dr-1. One has several of the red and partially red aircraft of the Red Baron. The other has Lothar's aircraft as one of the choices.