Chamberlain’s supplemental lexicon was devised to fill the gap between LSJ and BDAG, since both resources have inadequate coverage of LXX vocabulary and word usage. It was specifically designed to build on BDAG, supplementing its numbering system where there is coverage in both lexicons. (An index shows which words are covered only in BDAG, only in Chamberlain, or in both.) So in Chamberlain you might have a word gloss numbered as 3, and to find definitions 1 and 2 you would have to consult BDAG specifically. However, since most NT lexicons will have similar coverage in terms of word meanings (without the depth of BDAG), Chamberlain can serve as a useful “gap-filling” supplement to any NT lexicon. The lower price obviously makes it an attractive alternative to the full LXX lexicons.
Chamberlain should not be considered as an abridged LEH. The author did, of course, consult LEH as he did his original work, but he operates under a different translational philosophy and often offers word meanings that differ somewhat from or are not covered in LEH. There is also a number of LXX variants covered in Chamberlain that have no coverage at all in the Rahlfs-based LEH. So it should be considered a valuable lexicon in its own right.
A good example of Chamberlain’s gap-filling potential can be seen in his entry for αἰχμαλωσία:
αἰχμαλωσία 1.b. (Babylonian) exile Ps 95:1; (Assyrian) Tob 1:3S. 2.b. community of exiles 2 Esdr 5:5; Ps 125:1; Is 1:27; Ezk 1:1; 3:11; of returned exiles 1 Esdr 5:67; 6:5ff; of exiles from another land (Elam) Jer 25:19; (Egypt) Ezk 29:14.‡
LSJ offers the glosses “captive” and “body of captives,” with two LXX citations. LEH has exactly the same glosses as LSJ, with an added gloss—“a band of prisoners,” with several LXX citations and a number of Hebrew equivalents.
Similarly, BDAG has “captive” and “prisoner of war,” with several LXX citations. Chamberlain alone includes the notion of exile, which seems prominent in many LXX contexts.
In full disclosure, I edited the book for Hendrickson Publishers, so my description, while I hope it is not shameless, may nonetheless have elements that sound like something of a “plug.”