Yea, brother, let me have joy of thee in the Lord - “By showing me this favor in receiving my friend and brother as I request.” The phrase “in the Lord,” here seems to mean that, if this request was granted, he would recognize the hand of the Lord in it, and would receive it as a favor from him.
Refresh my bowels in the Lord - The “bowels,” in the Scriptures, are uniformly spoken of as the seat of the affections - meaning commonly the upper viscera, embracing the heart and the lungs; compare the notes at Isaiah 16:11. The reason is, that in any deep emotion this part of our frame is peculiarly affected, or we feel it there. Compare Robinson’s Lex. on the word σπλάγχνον splangchnon See this illustrated at length in Sir Charles Bell’s” Anatomy of Expression,” p. 85, following Ed. London, 1844. The idea here is, that Paul had such a tender affection for Onesimus as to give him great concern and uneasiness. The word rendered “refresh” - ἀνάπαυσόν anapauson - means “to give rest to, to give repose, to free from sorrow or care;” and the sense is, that by receiving Onesimus, Philemon would cause the deep and anxious feelings of Paul to cease, and he would be calm and happy; compare the notes at Philemon 1:7.