What influence did the unification of Poland and Lithuania into a single state have on the course of the Livonian War?

The Livonian War lasted from 1558 to 1583, mainly between the Russian Kingdom and the Grand Duchy of Lithuania. At the first stage of the war, Russian troops won a number of victories, including taking Polotsk (1563).
The defeats from the Moscow troops forced the Grand Duchy of Lithuania to seek an alliance with the Kingdom of Poland, which was concluded in 1569 in Lublin. As a result, the union of the two states appeared – the Commonwealth, whose troops were able to turn the tide of the Livonian War, liberate Polotsk (1577) and emerge victorious from the war.