I have the Yamaha Big Bar and Memphis Shades Lowers.
When searching for images for Cobra Fatty bars, it looks like both the Big Bar and Cobra may have about the same clearance for lowers.
My problem is, I also have the Yamaha passing light mounted so my turn signals are relocated lower.
When mounted normal the Memphis Lowers hit. I mount them left side on the right and right side on the left. When mounting them this way, they curve forward rather than toward the rear giving me the needed clearance. When mounting them in this way, I turn the forks full left when mounting the left side. The lower just about touches the turn signal at the rear point and about 1/2" to the bar. When mounted, its hard to tell they are backwards.