Context Here is Important
The dative reflexive pronouns of Rom 14:7 need to be seen in parallel with the other datives that precede (and follow) it in the context of the passage. The key verse in understanding their meaning is back in Rom 14:4 (NKJV for all quotes):
Who are you to judge another’s servant? To his own master [τῷ ἰδίῳ κυρίῳ] he stands or falls. Indeed, he will be made to stand, for God is able to make him stand.
The datives in that verse reflect that the actions one does are ultimately done "to" one's own (ἰδίῳ) master's (κυρίῳ) judgment, no others. One's actions either stand or fall in the master's opinion. Note that the word "master" here is the same word as "lord," so it could be translated in v.4 "to his own lord he stands or falls."
This concept gets extended in vv.5-6:
5 One person esteems one day above another; another esteems every day alike. Let each be fully convinced in his own mind. 6 He who observes the day, observes it to the Lord [κυρίῳ]; and he who does not observe the day, to the Lord [κυρίῳ] he does not observe it. He who eats, eats to the Lord [κυρίῳ], for he gives God thanks; and he who does not eat, to the Lord [κυρίῳ] he does not eat, and gives God thanks.
Their are four plain datives (κυρίῳ) in v.6 that relate to the statement of v.4-5. Whether people observe particular days or not, or whether they partake of eating or not, they do so "to the Lord." The article is not present in the Greek, and one could translate it as "to a lord," or even as v.4 translated in the NKJV, "to a master," i.e. to whoever that one is observing the day or not for or eating or not for approval of his judgement. Yet clearly the context is to believers in the church of Rome, and it is "the Lord" that Paul is speaking of here, for he intersperses God in the context.
So Rom 14:7 (the verse in question) and v.8 continues from this context:
7 For none of us lives to himself [ἑαυτῷ], and no one dies to himself [ἑαυτῷ]. 8 For if we live, we live to the Lord [τῷ κυρίῳ]; and if we die, we die to the Lord [τῷ κυρίῳ]. Therefore, whether we live or die, we are the Lord’s.
The parallel remains, such that the statement in v.7 is referring to the fact that no one lives or dies to be judged of themselves. That is, a person does not do what they do in life to then judge themselves about what they have done, nor do they do what they do at the time that they die to then judge themselves about what they gave their life for.
The statement of v.7 is proclaiming a rhetorically obvious truth (in the context of being judged); we will not judge our lives and our death. Another will judge them for their lives and deaths, that is "the Lord" (here with the definite article). They are judged of the Lord because they belong to the Lord (v.8), and so will be judged by Christ (v.9-10).
The idea is "to," for the parallel idea is "to whom is one looking to be judged" for his/her life (and all aspects of living out that life) and death? Not to him/herself, but to Christ the Lord, the master Who is served.