The phrase in the Lord’s service is literally “in the Lord” (see vv. 3 and 9); while for the Lord is also literally “in the Lord,” and may be taken with the same sense as the previous phrase.
Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on Paul’s Letter to the Romans. (UBS Handbook Series). New York: UBS, 1973. For this and other handbooks for translators see here .