Lord Damley probably provokes the English Civil War a bit on the early side as he wouldn't be the dove James II was, or trying to avoid conflict the way Charles I was.
Maybe his son, by some other woman, is the James II analog who receives a pension from Elizabeth I?
Either way, whether it's Damley as Henry IX or his son, it comes down to how they view divine rights of kings and religious liberty, issues of the ECW, and whether or not they piss off Spain and get involved in the Thirty Years War on the continent.
The worse things go for England, the better they go for Scotland because England is too distracted to try and gobble up Scotland. Unless things go very, very bad and the ECW expands beyond just some fleeing remnant armies trying to take a Scottish border fort as a base to regroup and attack back into England.