The thing is about the Commonwealth is that Lithuania was making appeals to Poland during Sigismund II's reign and he was making a push for a real union. There was already a personal union and dynastic union between the two prior to the Union of Lublin in 1569. The one thing that was holding back negotiations prior to his death was the szlachta, as they wanted better terms for themselves. I am not sure if Ivan IV would have been willing to make a better deal with Lithuania and, in my opinion, seemed to be pretty set on what he was going to do with them. What if negotiations stopped after the delegation under Mikołaj Radziwiłł left in March and were not continued as in OTL?