This is a fine example of Mary’s irony: She tells about two kings who were mortal enemies, but Lemuel accepted them both equally, regardless of their opposing political and religious leanings.
James II (1685-88) was a Catholic, a fact that caused much concern among the Protestant power brokers of his time. Both factions claiming to have the better understanding of God’s will, they tried to settle their disagreements by killing as many of their opponent’s people as possible.
Sadly, without reaching any theological conclusion.
So the English Protestants called the Dutch Protestants for help, and this changed the power balance and convinced James II to flee to France, where God was Catholic and thence he had great time in the court of Louis XIV (paying for it by what he managed to plunder before his hasty departure from England.)
His successor, William III (1650–1702) was a Protestant. Born ‘Prince of Orange,’ he was Stadtholder from 1672 over a number of Dutch provinces. (When, negotiating with Louis XIV and rejecting defeat, William III promised to “die, defending The Netherlands in the last ditch,” most likely expecting his soldiers to do the dying bit.)
In 1689, when William III was invited by the English Protestant power brokers to chase away James II he insisted that in return, he will replace him as the King of England, Ireland and Scotland, using different numbers in each place: William II and III. Probably to confuse the opposition. In Northern Ireland and Scotland he was rather disrespectfully called "King Billy" (which makes Billy Connolly - the II.)