FOR NOT ONE OF US LIVES FOR HIMSELF: oudeis gar hemon heauto ze (3SPAI):

"The truth is that we neither live nor die as self-contained units. " (Phillips)

In all of Scripture, there is no greater call for holy living and for submission to the sovereign and unconditional lordship of Jesus Christ. Paul's point is that whether one is a strong or or weak, a sincere believer feels free or not free to do certain things out of the same motive: to please his Lord. Neither one is more or less spiritual or faithful because of his convictions about practices such as those discussed above. Being "strong" in this sense is not synonymous with being spiritual, and being "weak" is not synonymous with being fleshly. The problem is that some believers of both persuasions thought themselves to be more spiritual and the others more fleshly. Paul’s whole purpose in these verses, and in the larger context of (Ro 14:1–15:13), was to disabuse believers of those false, divisive, and destructive notions.

AND NOT ONE OF US DIES FOR HIMSELF: kai oudeis heauto apothneskei (3SPAI): (9; ; 2 Corinthians 5:15; Galatians 2:19,20; Philippians 1:20-24; 1 Thessalonians 5:10; Titus 2:14; 1 Peter 4:2)

Paul asks the Corinthian saints...

Or do you not know that your body is a temple of the Holy Spirit who is in you, whom you have from God, and that you are not your own?  For you have been bought with a price: therefore glorify God in your body. (1 Corinthians 6:19,20)

J Vernon McGee comments that...

"not one of us lives for himself, and not one dies for himself" is generally quoted as a proof text that our lives affect others [Ed: in the sense of John Donne's "No man is an island."]. However, that thought is not in this passage. The truth is that we as Christians cannot live our lives apart from Christ. Whether you live, you will have to live to Him; whether you die, you will have to die to Him. Our Christian conduct is not gauged by the foods spread out on the table, but by the fact that our lives are spread out before Him. That is the important thing. One day we are going to have to give an account of the things we have done in this life." (Thru the Bible Commentary) 

Paul is saying that all believers, strong and weak, live out their lives accountable to God.

C H Spurgeon wrote...

FOR IF WE LIVE WE LIVE FOR THE LORD: ean te gar zomen (1PPAI) to kuriozomen (1PPAI):

"At every turn life links us to God, and when we die we come face to face with him. In life or death we are in the hands of God." (Phillips)

"For, whether we are living, with reference to the Lord we are living. Whether we are dying, with reference to the Lord we are dying. Therefore, whether we are living or whether we are dying, we belong to the Lord;" (Wuest)

What we do for other believers, we do not only for their sakes but for our Lord’s sake, because, whether we live or die, we are the Lord’s. Christ is our mutual Lord, our mutual sovereign; and therefore everything we do, even in our dying, should be to please and to glorify our sovereign Savior and Lord. He is our Owner; we are His slaves, His possessions. We live (and die) to serve Him, not to please ourselves. Since each believer belongs to Christ, it is out of place for strong to despise the weak or the weak to judge the strong concerning non-essential issues or matters not central to our Christian faith.

Stedman notes that Paul is

"not talking about funerals, and life and death in that sense. He is talking about those who feel free to enjoy liberty to the fullest. They are living, while others, because of deep convictions of their own, limit themselves, and to that degree they are dying, because death is limitation....The important thing is that we belong to the Lord. He understands." That, therefore, is what we ought to remember in our relationships with one another. We belong to the Lord. We are brothers and sisters. We are not servants of each other. We are servants of the Lord and he has the right to change us."

THEREFORE WHETHER WE LIVE OR DIE WE ARE THE LORD'S: ean te oun zomen (1PPAI) ean te apothneskomen (1PPAS), tou kuriou esmen (1PPAI): [Titus 2:14 Ro 14:7-9 1Co 6:19-20 2Co 5:15 2Pe2:1 1Pe 2:9; Rev 1:6;5:10 Ex 19:5 Dt 7:6; 14:2 Isa 43:21 Mal 3:17] (John 21:19; Acts 13:36; 20:24; 21:13; Philippians 2:17,30; 1 Thessalonians 5:10) (1 Corinthians 3:22,23; 15:23; 1 Thessalonians 4:14-18; Revelation 14:13)

FOR TO THIS END CHRIST DIED AND LIVED AGAIN: eis touto gar Christos apethanen (3SAAI) kai ezesen (3SAAI): (Isaiah 53:10-12; Luke 24:26; 2 Corinthians 5:14; Hebrews 12:2; 1 Peter 1:21; Revelation 1:18)

Christ’s death and resurrection are given as grounds for Him to exercise lordship over both the dead and the living:

THAT HE MIGHT BE LORD BOTH OF THE DEAD AND OF THE LIVING: hina kai nekron kai zonton (PAPMPG) kurieuse:  (Matthew 28:18; John 5:22,23,27-29; Acts 10:36,42; 2 Timothy 4:1; 1 Peter 4:5)

He might be Lord...

Paul explains in Ephesians that God manifested

the working of the strength of His might (This is the same mighty power) 20 which He brought about in Christ, when He raised Him from the dead, and seated Him at His right hand in the heavenly places, 21 far above all rule and authority and power and dominion, and every name that is named, not only in this age, but also in the one to come. 22 And He put all things in subjection under His feet, and gave Him as head over all things to the church, 23 which is His body, the fulness of Him who fills all in all. (Ephesians 1:19-23)

Writing to the Philippian church Paul explained that...

God raised him up to the heights of heaven and gave him a name that is above every other name, 10 so that at the name of Jesus every knee will bow, in heaven and on earth and under the earth, 11 and every tongue will confess that Jesus Christ is Lord, to the glory of God the Father. (Philippians 2:9-11)

We are not our own but Christ’s (1Co 6:19). This right of possession, and the consequent duty of devotion and obedience, are not founded on creation but on redemption. We are Christ’s because he has bought us with a price. In all of Scripture, there is no greater call for holy living and for submission to the sovereign and unconditional lordship of Jesus Christ. To deny the lordship of Jesus Christ in the life of any believer is to subvert the full work, power, and purpose of His crucifixion and resurrection. Christ's Lordship is the foundational truth for the unity of the Church amidst diversity of opinion.
 
Neither the strong nor the weak lives for himself or dies for himself, and for the same reason—both of them live for the Lord and both of them die for the Lord. What we do for other believers, we do not only for their sakes but for our Lord’s sake, because, whether we live or die, we are the Lord’s. Christ is our mutual Lord, our mutual sovereign; and therefore everything we do, even in our dying, should be to please and to glorify our sovereign Savior and Lord.      

Newell comments that...