Lightnings were reputed to be able to intercept SR-71s by flying ballistic profiles. They supposedly caught the SR-71s by surprise from overhead.
That's a myth, and if you read what has been written about the high-altitude zooms, particularly
by the pilots who flew them, it's clear that the Lightning was amost at a stand still at the top
and there's no way they could have maneuvered to engage, even with missiles. Also the max
zoom height achieved was just under 70,000', the SR-71A regularly operated 10 to 15,000' higher.
I personally believe that the source of the stories is confusion about the U-2 intercept tests, which
were done in the early '60s with the cooperation of the US, somehow these arranged tests, and a U-2
intercept in the early '80s, have been turned into 'we intercepted the SR-71'.