Romans 6

As Paul taught the necessity of faith and grace, he asked the Romans -

"WHAT shall we say then? Shall we continue in sin, that grace may abound?
2 God forbid. How shall we, that are dead to sin, live any longer therein?"  (New Testament | Romans 6:1 - 2)

In my mind, Paul is teaching that not only are we to repent (become "dead to sin"), but we must continue to strive to keep the Savior's commandments and repenting as necessary throughout our lives.  Nephi called this "enduring to the end" as he taught the "doctrine of Christ" where  he -

"...heard a voice from the Father, saying: Yea, the words of my Beloved are true and faithful. He that endureth to the end, the same shall be saved.
16 And now, my beloved brethren, I know by this that unless a man shall endure to the end, in following the example of the Son of the living God, he cannot be saved.
17 Wherefore, do the things which I have told you I have seen that your Lord and your Redeemer should do; for, for this cause have they been shown unto me, that ye might know the gate by which ye should enter. For the gate by which ye should enter is repentance and baptism by water; and then cometh a remission of your sins by fire and by the Holy Ghost.
18 And then are ye in this strait and narrow path which leads to eternal life; yea, ye have entered in by the gate; ye have done according to the commandments of the Father and the Son; and ye have received the Holy Ghost, which witnesses of the Father and the Son, unto the fulfilling of the promise which he hath made, that if ye entered in by the way ye should receive.
19 And now, my beloved brethren, after ye have gotten into this strait and narrow path, I would ask if all is done? Behold, I say unto you, Nay; for ye have not come thus far save it were by the word of Christ with unshaken faith in him, relying wholly upon the merits of him who is mighty to save.
20 Wherefore, ye must press forward with a steadfastness in Christ, having a perfect brightness of hope, and a love of God and of all men. Wherefore, if ye shall press forward, feasting upon the word of Christ, and endure to the end, behold, thus saith the Father: Ye shall have eternal life.
21 And now, behold, my beloved brethren, this is the way; and there is none other way nor name given under heaven whereby man can be saved in the kingdom of God. And now, behold, this is the doctrine of Christ, and the only and true doctrine of the Father, and of the Son, and of the Holy Ghost, which is one God, without end."  (Book of Mormon | 2 Nephi 31:15 - 21)

I believe that is what Paul was teaching the Romans saying -

"Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin."  (New Testament | Romans 6:3 - 6)

Adding -

"What then? shall we sin, because we are not under the law, but under grace? God forbid.
16 Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?
17 But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you.
18 Being then made free from sin, ye became the servants of righteousness."  (New Testament | Romans 6:15 - 18)

It becomes clear that there are conditions to receive "His grace".  Faith in Jesus Christ, repentance, baptism, receive the gift of the Holy Ghost and then continue to strive for righteousness or in other words strive to be like Him.