Sometimes if the lock is corroded, you may have to use a flathead screwdriver, miscut or blank key, or an inserted key pulled out one step, in order to get the cylinder started spinning.
If the cylinder is being rather difficult to remove, try loosening the two mounting screws on the adams rite lock body. Sometimes the through holes are not drilled correctly, and the installer will screw in the cylinders/thumbturns, and then tighten down the mounting screws, binding up the cylinders.
Also- when loosening the cylinder or the set screw, if it is not budging, try to slightly turn in clockwise, and then back. Sometimes that is enough to break it free.
It can be rather fun if the set screw breaks
