(Thanks to @jeremytreat5 who inspired me to dig)
This usage occurs 6x: 2 Cor 13:11; Eph 6:10; Phil 3:1; 4:8; 1 Thess 4:1; 2 Thess 3:1.
It's furthest from end in Phil 3:1, but still some way to go in 1 Thess 4:1.
2 Cor 13:11 Λοιπόν, ἀδελφοί
Eph 6:10 Τοῦ λοιποῦ
Phil 3:1 Τὸ λοιπόν, ἀδελφοί μου
Phil 4:8 Τὸ λοιπόν, ἀδελφοί
1 Thess 4:1 Λοιπὸν οὖν, ἀδελφοί
2 Thess 3:1 Τὸ λοιπόν, προσεύχεσθε, ἀδελφοί
KJV has 'finally' for 5/6, but 'furthermore' for 1 Thess 4:1.
Then RV & its children (ASV, RSV, ESV) have 'finally' for all 6.
NIV has 'finally', 'further' & 'as for other matters' each 2/6.
Vulgate de cetero 'about the rest' 6/6
Syriac Peshitta mekkēl 'hereafter', 'therefore' 6/6
Coptic Sahidic ⲧⲉⲛⲟⲩ ϭⲉ 'so now' 4/6
Gothic þata anþar '(about) the other/rest' 4/6
(experts please improve my glosses)
It's best understood as meaning: 'This is what I have left to say'.
'This is not the end. It is not even the beginning of the end, but it is perhaps the end of the beginning.'