Just like first, personal Polish-Lithuanian Union, real union from 1569 also was result of fate of dynasty-this time Jagiellons were going to die out. Would Sigismund Augustus had a son, something as radical as OTL Union of Lublin would rather not happen, or would be significantly delayed. IOTL both King and nobility of Poland feared, that with the end of Dynasty ties between Poland and Lithuania would be broken. Future after death of Sigismund Augustus was uncertain, thus radical moves seemed to be necessary. In situation, when future of House of Jagiellon is secure King would be propably last person to push for real union. Jagiellons were hereditary rulers of Lithuania, when in Poland they were elective monarchs, hereditary Grand Duchy was their best guarantion to secure also their election to the Polish throne. Nobility (especially lesser/middle nobles) of Poland and, to the lesser degree, middle nobility of Lithuania, would still want union to be tightened, but without fear of totall dissolution of union after extinction of House of Jagiellon-not as much as IOTL. Lithuanian magnates obviously would oppose real union, like IOTL. So how would late 16th century looks like in Poland and Lithuania? Sigismund Augustus having son(s) would not ceede his hereditary rights to GDL to the Crown, for sure. Also Volhynia, Kiev and Podlasie remain in GDL. Statutes of Lithuania also could be a bit different (Sigismund would not like power of Grand Duke to be reduced). Royal election in Poland would likely change-instead of tiny clique of magnates, masses of nobility would elect king, like IOTL, but with title of Grand Duke remaining hereditary, elections would remain pure formality as long as there are male Jagiellons around. Political systems of both realms would remain distinct, but Lithuanian middle nobility would likely continue their struggle against great magnates. There is problem of Muscovite-Lithuanian war, but in 1569 situation of GDL was not as dramatic for such radical moves if dynasty is not going to die out. Poles could complain, but letting Lithuania to colapse would be purely suicidal decision, not that GDL was really on the edge of collapse in 1569 IOTL. So how would situation develop and how long could 'status quo' be maintained?