I agree with roofus and Bob. No matter how widely accepted a lexicon is, to uncritically accept whatever it says without question is only to perpetuate the errors of those who contributed to it if they have (whether unintentionally or because of theological bias) made any.
Now, since the New Testament was not written by Greeks but by Hebrew men using the Greek language, shouldn’t we expect the idioms and word-meanings found in the NT to be, in general, derived not from secular Greek literature, but rather from the Old Testament Scriptures? While I’m certainly not suggesting that 1st century secular Greek works should be disregarded as irrelevant, shouldn’t the LXX be considered more appropriate and useful in determining the meaning(s) that Christ and the authors of the NT (who, of course, were Jewish) would have ascribed to the words aion and aionios rather than, say, the works of a 4th century BC Classical Greek philosopher? I mean, assuming there was such a thing in existence in the 1st century as the Hebrew Bible translated into Koine Greek, shouldn’t it be one of the primary sources to which one should refer when trying to ascertain what a 1st century Jew most likely meant when he used the words aion and aionios in a work written in Koine Greek? Or am I missing something?
As far as the definitions of aionios provided by BDAG, I think the first definition given (“pertaining to a long period of time” that is past) could apply to the word as it appears in the LXX in a number of places (e.g., Job 22:15; Ps 24:7; Ps 24:9; Ps 77:5; Pro 22:28; Pro 23:10; Isa 58:12; Isa 61:4; Isa 63:11; Jer 6:16; Jer 18:15; Eze 26:20; Eze 36:2; Hab 3:6). But I wonder what definition of aionios BDAG would consider most appropriate when a time of limited future duration is in view? Because the LXX abounds with such examples (e.g., Gen 17:7; Gen 17:8; Gen 17:13; Gen 17:19; Gen 48:4; Ex 12:14; Ex 12:17; Ex 27:21; Ex 28:43; Ex 29:28; Ex 30:21; Ex 31:16; Ex 31:17; Lev 6:18; Lev 6:22; Lev 7:34; Lev 7:36; Lev 10:9; Lev 10:15; Lev 16:29; Lev 16:31; Lev 16:34; Lev 17:7; Lev 23:14; Lev 23:21; Lev 23:31; Lev 23:41; Lev 24:3; Lev 24:8; Lev 24:9; Lev 25:34; Num 10:8; Num 15:15; Num 18:8; Num 18:11; Num 18:19; Num 18:23; Num 19:10; Num 19:21; Num 25:13; 1Ch 16:17; Job 3:18; Job 10:22; Job 21:11; Job 41:4; Ps 76:4; Ps 78:66; Ps 105:10; Isa 24:5; Isa 55:13; Isa 60:15; Jer 5:22; Jer 18:16; Jer 20:17; Jer 23:40; Jer 25:9; Jer 25:12; Jer 51:39; Eze 35:5; Eze 35:9; Jon 2:6; Mic 2:9).
While some might see the remaining occurrences of aionios in the LXX as falling under the last two definitions provided by BDAG (e.g., Gen 9:12; Gen 9:16; Gen 21:33; Ex 3:15; 2Sa 23:5; Job 33:12; Job 34:17; Ps 112:6; Ps 139:24; Isa 26:4; Isa 33:14; Isa 35:10; Isa 40:28; Isa 45:17; Isa 51:11; Isa 54:4; Isa 54:8; Isa 55:3; Isa 56:5; Isa 60:19; Isa 60:20; Isa 61:7-8; Isa 63:12; Jer 31:3; Jer 32:40; Jer 50:5; Eze 16:60; Eze 37:26; Dan 4:3; Dan 4:34; Dan 7:14; Dan 7:27; Dan 9:24; Dan 12:2), I think even these examples can be understood as referring to temporary duration rather than endless duration in an absolute sense. At any rate, most would agree that, while long and indefinite duration is most likely in view in the former examples, endless duration in an absolute sense is not. So I’m not sure why we can’t understand aionios in Matt 25:46 (for example) to have the same or similar meaning as it has in the LXX translation of Num 25:13 or Jer 25:9.
I like the concluding definition for aionios found in The Vocabulary of the Greek Testament (edited by James Hope Moulton and George Milligan): “In general, the word depicts that of which the horizon is not in view, whether the horizon be at an infinite distance, or whether it lies no farther than the span of a Caesar’s life.” That is, the word stands for a “hidden” and indefinite duration of time, whether past or future. This seems to be the meaning of olam in the Hebrew Bible, and since aion and aionion seem to have been employed by the inspired writers of the NT as the Greek equivalents of this single Hebrew word, this definition would be most consistent. And as it seems likely that Jesus would’ve spoken Hebrew or Aramaic (at least, when he was speaking to his disciples, like in Matt 25:46), the word he would have used would have either been olam or alam.