The bog-standard title for God in the Latin Middle Ages isn’t rex, it’s dominus. That is, not what we would translate “king,” but “lord.” It’s an important enough title that even vernacular writers use “dominus” sometimes instead of their own word. Because to medieval people, addressing God as “Lord” was a deeply significant theological claim—especially in contrast to earthly authority. Borrowing from an earlier answer:

There are some neat things to be found in individual European languages. Medieval German, for example, mixes the Latin dominus with the German herr--which is more like "mister" or “master” than necessarily a noble title. And as Benjamin Arnold showed, for a good chunk of the Middle Ages, Latin chronicles just call all German rulers princeps regardless.

But there’s a deeper theological issue in question, one that medieval people absolutely did address. Which is: can we use terms of earthly authority to refer to God, and can we use terms that are euphemisms for God to refer to people? And, critically, what are the implications of doing so?

When Jerome translates the Vulgate with "dominus," the word is well in current vogue to talk about earthly dynastic power. At the time, dominus was often a particular reference to the head of a household as both head of family and master of slaves, with everyone placed inferior to him. Calling Jesus "dominus" is a very particular theological claim in this context.

And the reverse implications of it will come to bother 12th century theologian John of Salisbury, in fact. He's not so impressed by the 'willful tyranny' of contemporary earthly lordship. Thomas Bisson argues that John very deliberately skates away from using terms "dominatio" and "dominus" in his writing "which have for him the resonance of willful power such as he can safely attribute only to God." Willful is a key part of the theological claims implicit in dominus; it's the ability to make what you say into reality (through orders, through the laws of physics or in Bisson's argument about how much the 12th century actually sucked, through violence). So in John's case, the resistance isn't to calling God "Lord." God is Lord--the only Lord, the only one who ought to have that kind of effecting, willful power and might. An earthly ruler can be imperatrix (yes, empress) or princeps or dux or rex (two of which are also appellations for Christ, of course), but not dominus.

And then there are the direct ties between the lordship of Christ and the lordship of men. In the Rule of Benedict of all places, which helps govern monastic life throughout the Middle Ages, chapter 63 explains the position of the abbot within the community through the metaphor of Christ's lordship:

But the Abbot, since he is believed to represent Christ, shall be called Lord and Abbot, not for any pretensions of his own but out of honor and love for Christ.

This is coming out of the pastoral side of Christianity epitomized by the semi-contemporary Gregory the Great's description of the pope as the "servant of servants"--the idea of humble, giving, leading lordship. The ROB shows the importance of association and allegory/metaphor in shaping the medieval worldview. They were not sharply literalist in the sense that using the same title meant ascribing the same characteristics. But they did understand that the connotations of the title in one circumstance would be connotations of the title in other circumstances, just applied to the different context at hand.

Although, as we saw, the word "dominus" itself could mean rather different things depending on one's perspective.