How and why did Polish rule over the Ukraine "downwardly deviate" from Lithuanian rule?

First of all the sentence:

"Ukrainiains seemed to accept Lithuanian rule for over two centuries"

is an anachronism. There was no "Ukrainians" in the period you are talking about. Neither any "Belorussians" existed. What later became "Ukrainians" and "Belorussians" were descendants of that part of the population which was Orthodox by religion.

After the conquest of Rus principatities by the Mongols, this orthodox part of the population found itself partially in the Grand Duchy of Lithuania, and partially in the Kingdom of Poland.

I recall that the Grand Duchy of Lithuania, until it united with Poland in 1385 was not a christian state. This was the last pagan state in Europe. In the sense that the Grand Duke himself and a large portion of the population were pagans. They lived in the same state with Orthodox population, which probably made a majority, but this is not exactly known.

The kingdom of Poland was officially Catholic, but also had a large part of the Orthodox population. The union between Poland and the Grand Duchy begins in 1385 as a dynastic union. The Grand Duke baptized, married the Polish queen, their realms were loosely united, and strong efforts were made to convert the whole population to Catholicism. As one can expect, they succeeded with the pagan part of the population more than with the Orthodox part. With years the union became closer and closer, until at some point it was almost complete and the new state was called the Polish-Lithuanian Commonwealth (1569).

The state had a high degree of religious toleration (more than anywhere in Europe at that time, I suppose). Most of the ruling elite was Catholic, but there was a large Orthodox population, as well as Muslim, Jewish etc. Of course there were all sorts of frictions between confessions and people did not enjoy "equal rights" in the modern sense, but interests of minorities were protected by law. We can find several Orthodox among the highest state officials, military commanders, nobility and magnates ("oligarchs"). However it is true that the majority of nobility (zchlachta) was Catholic, and it was profitable for a career to convert to Catholicism.

The frictions apparently increased at the time of reformation. Gradually the relations between Catholics and Orthodox deteriorated, and this led to a disastrous civil war. Religion was not the only reason of this civil war. Provocation from Moscow also played a role. Moscow Princes suddenly declared themselves the "Sovereigns of all Russias", at the time when most of the "Russias" was a part of the Polish-Lithuanian Commonwealth. Poles never recognized this title.

There was also an uprising of the Orthodox peasantry against landowners (magnates), Cossacs fighting for their privileges, etc., that is a kind of "class struggle".

Now returning to your original question. Did Orthodox people feel better in the Grand Duchy of Lithuania than in Poland? I don't know any hard evidence for this. But this is possible.

In general, pagans are more tolerant to other religions than Christians. (Example: Roman empire. While it was pagan it was generally tolerant (of course there were frictions, like everywhere else. But in principle it was tolerant. There was no religious wars at least). After it became Christian, religious wars started, and eventually all other religions were eliminated.

One can conjecture that the same eventually happened in the Polish-Lithuanian Commonwealth. But this is only a conjecture, I do not know any hard evidence. And the very fact that "Ukrainians accepted Lithuanian rule" as opposite to "Polish rule" has to be proved.

By the way, in XVI century, the most used official language in the Lithuanian part of the state was a kind of old Russian (using Cyrillic). After the unification, it was gradually loosing competition to Polish and German. The reason must be clear.

One more remark. The Civil war led eventually to what Russian historians call the "Re-unification of Russia and Ukraine". This period (immediately after the "re-unification" is called in Ukrainian history the Ruin (collapse, destruction). The result was division of Ukraine into two approximately equal parts, one returned to Poland, another stayed with Russia. Only after the violent partition of Polish-Lithuanian Commonwelath in the end of XVIII century, both parts were united within the Russian empire. Thus I suspect that not all Ukrainians were so unhappy under the Polish rule.

Sources. Most of the sources I used are in Russian, Ukrainian and Polish, so I do not cite them. A good book in English is God's Playground by Norman Davies. The "civil war" that I mentioned is officially called "Khmelnicki uprising". When reading the books and other sources, please take into account that these questions are still hotly debated by nationalist historians and the views of many authors are strongly biased. Especially this applies to Russian and Ukrainian authors.