read current and old Dictionay articles on LXX, quotations [NT use of OT], read the
passage(s) in commentaries that use Greek and Hebrew. The resources here and current commentaries like WBC, NICOT, possibly those published by fortress press or anchor series could be helpful as well. Finally, you might have to seal the deal as to why the author used LXX rather than the Hebrew in that context. This would take serious careful study of the author's argument.
Of course this sort of goes beyond your Q on LXX but it is another step.
