For God is king over all the earth;
sing hymns of praise.
God rules over the nations;
God sits upon his holy throne.
(Ps 47:8)

Does the fact that Christ is king over humanity mean that the Father cannot also be Lord and king?

First of all the Kingdom of God is his Creation which he sustains and rules by his wisdom, power and providence. The Father created all things thorough his Son in the Spirit.

Some angels and mankind rejected the sovereignty of God in the beginning thus lost God's friendship and a participation in his kingdom. Although we abandoned God, God never abandoned us.

In the Old Testament Israel was called to accept the sovereignty of God through Moses who gave them the Laws of God's Kingdom. The Father is the origin of all things. Christ came from the Father to do the will of the Father, that is, to gather sinful humanity the Kingdom of God. Christ is the king over humanity in a special way because being God, he was also man. His kingdom is both visible and invisible. It is visible in all Christians who accept Christ as the divine Son of God yet invisible because it consists of all men of good will both on earth and in heaven. Christ's kingdom is subordinate to the Father as he taught us to pray, "Our Father who art in heaven, hallowed by thy name, thy kingdom come...."

Christ revealed the power of God's kingdom by healing the sick, raising the dead and casting out demons. Some Jews accused Jesus of casting out demons by the power of the devil. He said to them, "Every kingdom divided against itself will be laid waste.... And if Satan drives out Satan, he is divided against himself; how, then, will his kingdom stand? And if I drive out demons by Beelzebub, by whom do your own people drive them out? Therefore they will be your judges. But if it is by the Spirit of God that I drive out demons, then the kingdom of God has come upon you." (Mt. 12:25-28)

A human king can only be one person. The kingship of God is different because it is triune in nature. The Father acts through the Son in the Spirit. All the persons in God live in each other and act as one. All of them are sovereign, they have infinite wisdom, power and are eternal but exercise their divine sovereignty in different ways. The Father is king as the originator of all, the Son is king because he unites in himself divinity and humanity. The Holy Spirit in the Nicene Creed is called "the Lord, the giver of life, who proceeds from the Father and the Son." In what sense is the Holy Spirit Lord? "The Father sends the Holy Spirit in the power of his Fatherhood, as he has sent the Son; but at the same time he sends him in the power of Redemption accomplished by Christ--and in this sense the Spirit is sent by the Son: 'I will send him to you'". (Encyclical Letter "Dominum Et Vivificatem" by Pope John Paul II, May 1986,#8) The Holy Spirit is also Lord because of the intimate and eternal connection with the Father and Son.

At the end, the kingdom belongs to the Father, Through he Son, in the Spirit. Christ is gathering subjects for the kingdom of his Father in the power of the Spirit. The Son "Hands over the kingdom to his God and Father, when he has destroyed every sovereignty and every authority and power."(1 Cor.15:24)