The Western powers in the second half of the 16th century
After their defeat at Preveza in 1538 the powers constituting the Holy League, namely the Vatican, Venice, Genoa, the Hapsburg Empire and the state of the Maltese Knights had to face on the one hand the failure of their common effort and on the other hand internal problems each one in its own territory. Protestantism was spreading in Europe, weakening the Pope's power and fondling desires for political autonomy and revolutions, particularly in the state of the Hapsburgs. In 1565 they had to unite again in order to break the Ottoman siege against Malta, but they failed, since the Venetians deliberately delayed, unwilling to spoil their relations with the High Porte and the rest of the powers were late to make a move.
The change of course from inertia to action occurred when Pius V accessed the papal throne. The counter-reformist Pope was nostalgic of the Crusades' era and wanted to reinstate the supremacy of the Catholic Christian faith both towards Islam and towards Protestantism.
Pius V turned for help to Philip II, who controlled -among others- several parts of the Italian peninsula and Sicily. Although theoretically supportive of the Pope's project, Philip had to face on the one hand the revolt of the Moors in Spain and, on the other hand, the revolution in the Netherlands. Although he promised the Pope to provide help, he did so slowly and sparingly.
Also, the Pope's desire to include Venice in the League made him sceptical because Venetians were renowned for serving solely their own interests and did not hesitate to go back on their obligations. Finally all together did not trust the Genoese who had been charged with the defeat in Preveza, but continued to work -not without money- for the papal interests.