This is a good one. The modern English word lord has roots in the Old English word hlaf, which meant loaf as in a loaf of bread. What the Anglo-Saxons thought of as a lord was called hlafweard/hlaford, meaning loaf-keeper, or guy who's in charge of the food. You can see this used to refer to secular lords in texts like Judith or The Battle of Maldon. In Old English texts of the Bible, lord doesn't get associated with god, in the texts I've seen. Compare Genesis 3:9 versions:
Old English Text 'God clipode þa Adam, and cwæð: 'Adam, whær eart þu?'
King James Version And the LORD God called unto Adam, and said unto him, Where art thou?
In most Old English texts, they simply call god by the Old English word God. A lot of Old English religious verse also includes Latin interwoven, in which case the Latin word Dominus comes up about as much. By the early 13th century early Middle English text of Ancrene Wisse, Laverd (read the v as a u) had come into use to mean God: ". . . alle hare sares setteth in ower heorte ant siketh to ure Laverd . . ." And in that case, it's very clearly referring to the Big Man Upstairs. So the word Lord clearly had its roots in secular leaders, but somewhere along the way, it starts getting applied to religious contexts, too. As for the exact reason why and when, I can't say, but I'd love any Anglo-Saxonists out there to help out. The Latin Dominus is more ambiguous than the OE God, so it may be that later translators started getting Lord out of Dominus as the word Lord picked up more formal connotations (Edward I probably wouldn't have appreciated being called Bread Master), but that's just my guess.
Sources:
/u/rimeroyal focused very specifically on the English word lord, and I agree 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 a noble title.
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 lord can be 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. But to your question, OP: 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.