16 It may also be required, when it has not been said, if you sleep in the lots, but “in the midst of the lots;” what this is, “in the midst of the lots.” Which expression indeed, if more exactly it were translated from the Greek, would signify, “in the midst between the lots,” which is in no one of the interpreters I have read: therefore I suppose, that what has been said signifies much the same, to wit the expression, “in the midst of the lots.” Hence therefore what seems to me I will explain.
Ofttimes this word is wont to be used for uniting and pacifying one thing and another, that they may not mutually disagree: as when God is establishing His covenant between Himself and His people, this word the Scripture uses; for instead of that expression which is in Latin between Me and you, the Greek has, in the midst of Me and you. So also of the sign of Circumcision, when God speaks to Abraham, He says, “There shall be a testament between Me and you and all your seed:” which the Greek has, in the midst of Me and you, and the midst of your seed.
Also when He was speaking to Noe of the bow in the clouds to establish a sign, this word very often He repeats: and that which the Latin copies have, between Me and you, or between Me and every living soul, and whatever suchlike expressions there are used, is found in the Greek to be, in the middle of Me and you, which is ‡ νὰ μ·σον. David also and Jonathan establish a sign between them, that they may not disagree with a difference of thought: and that which in Latin is expressed, between both, in the middle of both, the Greek has expressed in the same word, which is ‡ νὰ μ·σον.
But it was best that in this passage of the Psalms our translators said not, “among the lots,” which expression is more suited to the Latin idiom; but, “in the midst of the lots,” as though “in the midst between the lots,” which rather is the reading in the Greek, and which is wont to be said in the case of those things which ought to have a mutual consent....But why in the “lots” the Testaments should be perceived, though this word is Greek, and the Testament is not so named, the reason is, because through a testament is given inheritance, which in Greek is called κληρονομία, and an heir κληρονόμος Now κλῆρος in Greek is the term for lot, and lots according to the promise of God are called those parts of the inheritance which were distributed to the people. Whence the tribe of Levi was commanded not to have lot among their brethren, because they were sustained by tithes from them.
For, I think, they that have been ordained in the grades of the Ecclesiastical Ministry have been called both Clergy and Clerks, because Matthias by lot was chosen, who we read was the first that was ordained by the Apostles. Henceforth, because of inheritance which is given by testament, as though by that which is made that which makes, by the name of “lots” the Testaments themselves are signified.
Source: The Enarrations, or Expositions, on the Psalms (New Advent)