What about this for a theory (off the top of my head):
a lot of the Test teams Lillee played against in the 70s and 80s were stronger than a lot of the sides Donald played against in the 90s an 00s (remembering the last 7 years are supposedly the worst ever for test cricket or something, aren't they?)
Seems to me England were better in the 70s and early 80s than they were in the 90s and the 00s; WI were infinitely stronger; Pakistan were pretty competitive (the side they sent out here in 76-77 was none too shabby) - probably on a par in terms of batting line ups with the ones Donald bowled to if not better; India would probably have been better in the 90s, but the 70s-80s India with Vengsakar, Gavaskar and Viswanath was pretty damn good too and it would be a toss up. Would agree NZ not that great in the 70s compared with 90s.
Some of the names DK bowled to - Lloyd, Greenidge, Haynes, Richards, Kalicharan, Richardson, Rowe, Dujon, Gavaskar, Vishy, Vengsakar, Zaheer Abbas, Javed Miandad, Majid Khan, Imran Khan, Gower, Botham, Boycott, Knott - they're storied cricketers in the annals of the game. It was a great era, and his being a dominant figure in an era of so many household names in cricket history may be a reason why people look on him as a better bowler.
The dominant side in Lillee's era (apart form Australia in the mid-70s, which he had a lot to do with) was the Windies, against whom he averaged 27 ish, and that includes the 1972 series where he played one test, didn't take a wicket for 132 and broke down with stress fractures. Take out that one test, and he averaged 25 against one of the great batting line ups of all time.
Donald's average vs Australia, the dominant side in his era, is 31, so not a huge difference between the two of them - 4 runs per wicket overall, 6 if you take out the errant test of Lillee's in 1972. It's not like Donald averaged 60 or something against Australia and that's a point of difference.
One thing I wonder about is if Lillee's deeds getting Australia home or setting up an Aussie win have a lot to do with his perception compared with that of Donald. When I think of the two, they both had wonderful actions, both bowled at high speed, both made the ball talk.
But when I think of Lillee, I always think of moments like the Centenary Test at Melbourne (6 for 26 defending 120 odd then 5-139 in the 2nd dig to win the game for us); 74-75 and 75-76 with Thommo; that spell at the end of day 1 in Melbourne when he bowled Viv off the last ball then came back next day and finished with 7 for; his spell in Perth v the World XI; the look of fear in the eyes of even very good players when they faced him and his dander was up with the crowd behind him; his partnership with Thommo in the 75 WC final; his duels with Javed (not the idiotic kicking incident, but actually with the ball); 5 for on debut v England; 5 for 15 off 15 v England at Birmingham in 1975; 31 wickets in 1972 Ashes, then 39 in the 1981 Ashes (in a well beaten team); beating Botham 5 balls in a row then walking down the pitch aftert he last time and saying "Look Beefy, just hang the bat there and let me try and hit the bloody thing will you?"; and his bowling long spells in even the hardest conditions.
Now I'm not saying that Donald did not or could not produce things like that, because he was a truly great bowler as well, but those are the things I'll always take with me when I think of Lillee.
Sadly, the first thing that comes to my mind when I think of AD is that tragic run out in the WC semi of 99, and that's not fair. But it's what springs to mind, and I wonder whether the juxtaposition of their team's achievements and their personas may have combined to some extent to have Lillee shade AD in a lot of peoples' minds when there may not be that much between them, if anything.
So I don't think you could say Donald lacked heart and Lillee puffed out his chest and that was the difference. If puffing out your chest and being macho was the key to it, Andre Nel would be the greatest bowler of all time. No one should denigrate either of these great bowlers by making such a trite observation as that. They both had their own personas, and both were wonderfully effective bowlers.
It's not always a question of raw analysis of figures which you point to in saying one fella was a better bowler than the other. If you filter their records, overall there is very little between them in their averages in matches won, matches lost and overall. All I can say is that I saw a fair bit of both of them live and on TV/ film, and I would say there is very little between them but I would go for Lillee - just.
On watching Lillee and others from the 70s and earlier on film, I so wish we had the camera angles and technology we have now. Just to be able to look at, for example, some of that 1972 footage where you see Massie or Lillee bowling from behind the keeper and the replays are all blurry - you'd get such a better idea of the amount of swing they got and of them in general if you could compare apples with apples. Likewise having the radar on some of the fellas form the 70s and 80s in their pomp would have been very illuminating - especially Thommo pre-shoulder, Lillee pre-back and Holding, Imran and Croft in general to name but a few.
God it was a great era - I know, I was there, I saw it.