Depends upon how you define "Better". Was the Lightning better in the one specific role it was designed for (point defence of the V bomber bases)? Undoubtedly (and in case you were wondering, I'm a big fan of EE's finest). Was the Lightning better in terms of it's adaptability or operational flexibility beyond that narrow role? Absolutely not. As for the Mirage III being drastically inferior, in raw performance terms, that simply isn't the case. Sure, if you want to get to FL50 & 650 knots IAS as quickly as possible, nothing really touches the Lightning until the mid 70's but the Mirage isn't "Drastically" far behind as you state. For starters, it has an awful lot more aerodynamic lift to play with which, to a greater extent than you seem to believe, partially offsets the sheer grunt of those two Avons. Above 10,000 ft or so, the Lightning won't be achieving anywhere near the 50,000 ft/min initial climb rate and nor will the Mirage be anywhere near it's own baseline figures. The Mirage will, however, have a flatter performance curve due to the extra lift from the large delta planform. Furthermore, once it's there, a Mirage is going to be burning less fuel not only as it's one engine vs two but also because that extra lift requires less thrust to maintain altitude. Dassault didn't manage to sell 1,400 of the things without good reason you know - it wasn't drastically inferior to anything. Imagine what a militarised FD 2 might have achieved with the higher thrust and greater efficiency of the Avon in a similar airframe.
As for the RAF not requiring a lightweight fighter - bomber to replace their Venoms in the late fifties / early sixties, why then, are Hawkers converting all those Hunter F 4's & F 6's (also with range / payload issues) into FGA 9's??
I'm struggling to understand what the small radar / shit AAM's thing is all about. Had the FD 2 been developed, it wouldn't have had the Cyrano / R530 fit that the Mirage had. Rather, it would surely have had AI 23 (a small yet capable little set) and Red Top (arguably, the world's most advanced and capable AAM of ANY type, let alone IR guided in period).
I love the Lightning, I really do and I miss the thrill and spectacle of seeing them fly but, with the benefit of hindsight, I can't help but think it was the wrong (albeit the only realistic) choice of airframe. The Sandys future never came to pass - manned fighters are still with us today and as that reality became clear in the mid / late sixties, it rather left the Lightning as an evolutionary dead end with no place left to go*.
Regards,
Frank
* Really, despite the line drawings, the scale models, the VG proposals etc the airframe just isn't going any further down the development path. It's too constrained by the original design parameters and by the time development is either desirable or necessary, there are better solutions available.