That is the question I received online from someone Saturday. I thought it was an important one, deserving as an exhaustive but clear response as I could give. The importance of Christ's Lordship drives me to post my response here:
______________
The answer to your question is a single "Yes". Though I may not be the best to answer the question, I can tell you what the "catholic" church (that is, the universal church) has believed through the ages as contained in the
Westminster Larger Catechism.

I've found the following to be helpful to your question:
Question 36
Who is the Mediator of the covenant of grace?
Answer 36
The only Mediator of the covenant of grace is the Lord Jesus Christ, who, being the eternal Son of God, of one substance and equal with the Father, in the fullness of time became man, and so was and continues to be God and man, in two entire distinct natures, and one person, forever.
Question 37
How did Christ, being the Son of God, become man?
Answer 37
Christ the Son of God became man, by taking to himself a true body, and a reasonable soul, being conceived by the power of the Holy Ghost in the womb of the virgin Mary, of her substance, and born of her, yet without sin.
Question 38
Why was it requisite that the Mediator should be God?
Answer 38
It was requisite that the Mediator should be God, that he might sustain and keep the human nature from sinking under the infinite wrath of God, and the power of death; give worth and efficacy to his sufferings, obedience, and intercession; and to satisfy God's justice, procure his favor, purchase a peculiar people, give his Spirit to them, conquer all their enemies, and bring them to everlasting salvation.
Question 40
Why was it requisite that the Mediator should be God and man in one person ?
Answer 40
It was requisite that the Mediator, who was to reconcile God and man, should himself be both God and man, and this in one person, that the proper works of each nature might be accepted of God for us, and relied on by us, as the works of the whole person.
Question 45
How does Christ execute the office of a king [I think this could be translated Lord]?
Answer 45
Christ executes the office of a king, in calling out of the world a people to himself, and giving them officers, laws, and censures, by which he visibly governs them; in bestowing saving grace upon his elect, rewarding their obedience, and correcting them for their sins, preserving and supporting them under all their temptations and sufferings, restraining and overcoming all their enemies, and powerfully ordering all things for his own glory, and their good; and also in taking vengeance on the rest, who know not God, and obey not the gospel.
Question 51
What was the estate of Christ's exaltation?
Answer 51
The estate of Christ's exaltation comprehends his resurrection, ascension, sitting at the right hand of the Father, and his coming again to judge the world.
Question 52
How was Christ exalted in his resurrection?
Answer 52
Christ was exalted in his resurrection, in that, not having seen corruption in death (of which it was not possible for him to be held), and having the very same body in which he suffered, with the essential properties thereof (but without mortality, and other common infirmities belonging to this life), really united to his soul, he rose again from the dead the third day by his own power; whereby he declared himself to be the Son of God, to have satisfied divine justice, to have vanquished death, and him that had the power of it, and to be Lord of quick and dead: all which he did as a public person, the head of his church, for their justification, quickening in grace, support against enemies, and to assure them of their resurrection from the dead at the last day.
Question 53
How was Christ exalted in his ascension?
Answer 53
Christ was exalted in his ascension, in that having after his resurrection often appeared unto and conversed with his apostles, speaking to them of the things pertaining to the kingdom of God, and giving them commission to preach the gospel to all nations, forty days after his resurrection, he, in our nature, and as our head, triumphing over enemies, visibly went up into the highest heavens, there to receive gifts for men, to raise up our affections thither, and to prepare a place for us, where himself is, and shall continue till his second coming at the end of the world.
Question 54
How is Christ exalted in his sitting at the right hand of God?
Answer 54
Christ is exalted in his sitting at the right hand of God, in that as God-man he is advanced to the highest favor with God the Father, with all fullness of joy, glory, and power over all things in heaven and earth; and does gather and defend his church, and subdue their enemies; furnishes his ministers and people with gifts and graces, and makes intercession for them.
(copied from http://www.studylight.org/his/ad/cac/cat/westminsterlg.html)
If you are seriously considering the question about Christ's Lordship, I would like to send you a copy of The Westminster Larger Catechism: A Commentary, by Johannes G. Vos. It gives Scripture references to all of the questions above, as well as short commentaries on each point within the answer. I find it very helpful.

Another helpful book about knowledge of God in general is John Frame's
The Doctrine of the Knowledge of God. It is an amazing book on epistemology (the study of knowing). I would be happy to send you a copy of this as well, but will give you the beginning of Chapter One: God, the Covenant Lord to help answer your main question:
Who is this God that we seek to know? Scripture described Him in many ways, and it is dangerous to seize on any of them as being more basic or more important than others. In seeking to summarize the Scripture's teachings, however, we can certainly do worse than to use the concept of divine "lordship" as our point of departure. "Lord" ( Yahweh in Hebrew) is the name by which God identified himself [sic] at the beginning of His covenant with Israel (Exod. 3:13-15; 6:1-8; 20:1f.). It is the name (kurios in Greek) that has been given to Jesus Christ as head of the New Covenant, as head of His redeemed body (John 8:58; Acts 2:36; Rom. 14:9). The fundamental confessions of faith of both testaments confess God--Christ--as Lord (Deut. 6:4ff.; Rom. 10:9; 1 Cor. 12:3; Phil. 2:11). God performs His mighty acts "that you may know that I am the Lord" (cf. Exod. 7:5; 14:4, 18; the references in the Introduction; and Pss. 83:18; 91:14; Isa. 43:3; 52:6; jer. 16:21; 33:2; Amos 5:8). At critical points in redemptive history, God announces "I am the Lord, I am he" (Isa. 41:4; 43:10-13, 25; 44:6; 48:12; cf. 26:4-8; 46:3f.; Deut. 32:39f., 43; Ps. 135:13; Hos. 12:4-9; 13:4ff.; Mal. 3:6, which allude to Exod. 3:13-15). In such passages, not only "Lord" but also the emphasis on the verb "to be" recall the name-revelation of Exodus 3:14. Jesus also frequently alludes to the "I am" in presenting His own character and office (John 4:26; 8:24, 28, 58; 13:19; 18:5ff.; cf. 6:48; 8:12; 9:5; 10:7, 14: 11:25; 12:46; 14:6; 15:1, 5). One of the most remarkable testimonies to Jesus' deity is the way in which He and His disciples identified Him with Yahweh of Exodus 3--a name so closely associated with God that at one point the Jews became afraid even to pronounce it. To summarize these points: throughout redemptive history, God seeks to identify himself to men as Lord and to teach and demonstrate to them the meaning of that concept. "God is Lord"--that is the message of the Old Testament; "Jesus is Lord"--that is the message of the New. (NOTE: Frame doesn't small cap the Scripture references. I took the liberty to edit them into a smaller font.)
_____________
I don't know how helpful my answer was to the questioner, but it did wonders for my own heart to review this precious doctrine.
-w