Is there an aircraft in service today with a better rate of climb than the B.A.C Lightning?

BAC Lightning? It was an English Electric Lightning when I were lad stood at Usworth Airfield in the 1960's watching the Sunderland air display when one went into a vertical climb. It was capable of mach 2 in a vertical climb - without an After burner.

Virtually every fast jet in service today has an equal, or better climb than the EE Lightning. Here are just a few examples:

Su-35: 55,100ft

Eurofighter Typhoon: >62,000ft

Mig-29: 65,000ft

Rafale: >60,000ft

Quite a few actually. The BAC Lightning is quite underpowered compared to modern aircraft like the F-15, F-16 and SU-27 and SU-33, not to mention the F-22.

According to the operating data manual, the official rate of climb of the lightning was 20,000ft/min (initial climb rate was 50,000ft, but it clearly slows at higher altitudes). The F-15 has a climb rate of ,50,000ft, and the Eurofighter 60,000ft/min F22 is said to be 55,000ft/min

A few but it is still the fastest plane the RAF have ever had

no. surprisingly no one ever managed to produce an aircraft since 1950ies.