Swedish King Eric XIV was obsessed about Liz IOTL, but all his attempts to marry her failed ,and the very fact, that he tried to get her hand caused lots of troubles for him, for example it ruined his other marriage plans, like when he tried to get hand of Hessian princess, but at the same time he was sending letters to Elizabeth (still hoping to get her attention) convincing her, that his Hessian marriage plans are not serious. His letters were captured by Danes, who quickly made use of them, sending copies to Eric's would-be father-in-law and other German monarchs, ruining his reputation. So what if Tudor-Vasa marriage really happen? What should be changed to make it possible? Perhaps longer living Edward VI would let his sister marry fellow Protestant monarch? How would Liz fare as Queen consort of Sweden? Would she dominate her husband (thus eliminating influence of Joran Persson, who was power behind the throne IOTL). Would Eric's downfall be avoided? Perhaps his menthal health would not deterioriate as much as IOTL and thanks to Elizabeth some of his disastrous decisions would be avoided (like Sture family murder). Also Eric's conflict with younger brother should not be as bad as IOTL (Erik was jealous, that Johan married woman from Royal house, while his own attempts to marry woman of royal blood failed).