How do Catholics understand how the title “Lord” for Jesus is dependent on his resurrection at Ro 14:9 if it means he is God? Romans 14:9 For to this end Christ both died, and rose, and revived, that he might be Lord both of the dead and living (KJV)


How does being revived (lived again, ASV) make him Lord of both the dead and the living?   

Catholics appear to teach that after Pentecost Christians understood that calling Jesus Lord was the same as calling him God.


  In the Gospels, Jesus is rarely called "Lord", with the exception of a few times in Luke and John. The Apostles and first disciples did not come to the full realization that Jesus was God until after his Resurrection and after they had received the Holy Spirit at Pentecost. Once they had reached that realization they did not hesitate to attribute to him the divine title of "Lord" as used in the Old Testament. (Catholic Education Resourse Center)
The argument that calling Jesus "Lord" necessarily or always refers to his divinity, I suspect, is a novel one; and non-magisterial catechetical resources carry no guarantee of the soundness of their argumentation for doctrine, since the deposit of faith was handed on largely without explanation of the doctrines, containing only the doctrines themselves: various explanations and arguments for said doctrines' validity accumulating over time. That said, there are certain instances which make it clear that for early Christians, the lordship of the Messiah, and his divinity, were without scruple conflated and mingled into one conception of one single person, one divine Messiah - inasmuch as that's precisely who Jesus is in the New Testament: "God ..  made flesh." (John 1). One key example is, "My Lord and my God!" (John 20:28). Or the instances of "The Day of the Lord" being conflated with the "Day of Christ." Yahweh the only Saviour with Jesus the Saviour of all. Etc. Clearly "Lord" with reference to Jesus is directly calling Him God, as in the Lord of all.

Consider two chapters prior:


  Romans 10:9-13 (DRB) For if thou confess with thy mouth [that Jesus is Lord], and believe in thy heart that God hath raised him up from the dead, thou shalt be saved. 10 For, with the heart, we believe unto [righteousness]; but, with the mouth, confession is made unto salvation. 11 For the scripture saith: Whosoever believeth in him, shall not be confounded. 12 For there is no distinction of the Jew and the Greek: for the same is Lord over all, rich unto all that call upon him. 13 For whosoever shall call upon the name of the Lord, shall be saved.


St. Paul quotes Joel 2:32 here:


  And it shall come to pass, that every one that shall call upon the name of the Lord [Yahweh] shall be saved: for in mount Sion, and in Jerusalem shall be salvation, as the Lord hath said, and in the residue whom the Lord shall call.


Thus, Romans 14:9 might rightly be understood in the sense that God in some sense can become 'more' the Lord of the living and the dead by partaking of life and death in the humanity of Christ, than if He hadn't - and only in that sense. Analogous to how Hebrews 4:15 describes the incarnation (Phil. 2):


  For we have not a high priest, who can not have compassion on our infirmities: but one tempted in all things like as we are, without sin.


On the one hand, not having compassion on our infirmities wouldn't follow from not being human, since God can make Christ quite capable of sympathizing with those who were, according to Hebrews 1, and John 1, were created through him, and which all consist in him (Col. 1:17).


  Hebrews 2:17-18 (DRB) Wherefore it behoved him in all things to be made like unto his brethren, that he might become a merciful and faithful high priest before God, that he might be a propitiation for the sins of the people. 18 For in that, wherein he himself hath suffered and been tempted, he is able to succour them also that are tempted.


As if Christ, who is greater than the angels, couldn't do what angels an do. Thus the argument is that it is fitting and a way in which He can in yet another way be considered the perfect mediator, not that if He lacked humanity, He couldn't save another way, for example.

As with Romans, the author of Hebrews has already called Him God:


  Hebrews 3:1-4 (DRB) Wherefore, holy brethren, partakers of the heavenly vocation, consider the apostle and high priest of our confession, Jesus: 2 Who is faithful to him that made him, as was also Moses in all his house. 3 For this man was counted worthy of greater glory than Moses, by so much as he that hath built the house, hath greater honour than the house. 4 For every house is built by some man: but he that created all things, is God.


There is as much difference between God and some man as there is between Christ and Moses. Why? Because He is God in the flesh. A man, yes, but who is that man? Son of Mary, or Son of God first, "from ancient times, even from the days of eternity?" The latter.

The word translated "[that] he might be lord of both" is a single verb in the Greek (κυριευση), meaning, "he might be lord." This never refers to being a particular lord or the Lord, but to *the quality of having or exercising governance over*, or exercising one's lordship over someone or something. It doesn't refer to becoming Lord.

However, here, even with the Catholic or trinitarian conception of Jesus, this clearly refers to the humanity of Christ ("he died and rose" etc.) and not to his divinity, in which He is already Lord by virtue of His being God. Here, Christ becomes the lord of the living and the dead by buying them from sin, and being "the Saviour of all men" (1 Tim. 4:10).

St. Paul's point in most or all of these instances is that Jesus is Lord in every way imaginable - as both God and as man. King and Lord in the sense of the new Adam and Messiah as well as in the sense of God.