CANON 16That and public relations:
It is beyond doubt that ecclesiastical honors are bestowed not in consideration of blood relationship but of merit, and the Church of God does not look for any successor with hereditary rights, but demands for its guidance and for the administration of its offices upright, wise, and religious persons. Wherefore, in virtue of our Apostolic authority we forbid that anyone appropriate or presume to demand on the plea of hereditary right churches, prebends, deaneries, chaplaincies, or any ecclesiastical offices. If anyone, prompted by dishonesty or animated by ambition, dare attempt this, he shall be duly punished and his demands disregarded.
CANON 6
We also decree that those who in the subdiaconate and higher orders have contracted marriage or have concubines, be deprived of their office and ecclesiastical benefice. For since they should be and be called the temple of God, the vessel of the Lord, the abode of the Holy Spirit, it is unbecoming that they indulge in marriage and in impurities.
Take a look at the Wikipedia article on the history of clerical celibacy. The requirement for clerics to abstain from serial realtions goes back long before Lateran II, to the early 4th Century council of Elvira in Spain.