> Apparently it could intercept at 65000ft

Reportedly it intercepted a USAF RB-57F[1] at 80,000ft and also did a zoom climb to just under 88,000ft.

https://theaviationgeekclub.com/raf-lightning-pilot-recalls-...

[1] A reconnaissance aircraft based on the English Electric Canberra. NASA still flies a couple of them for high altitude research.