Is the Noo F-35 Jump Jet (another awful 60s press term!) called a Lightning II after the P-38 (which I get confused with the Westland Whirlwind, not the chopper of the same name) or the EE version? and should it be a Lightning III?
As per my post in the Interesting Planes thread, it's named after the P-38. It is a Leftpondian-designed plane after all...
and it looks more like a Dyson than a Harrier in hover mode
That's what comes of trying to get STOVL capability
and supersonic performance in the same aircraft. Thrust is a function of the mass of gas ejected and its velocity - the Harrier's Pegasus engine had a lot of thrust courtesy of a high mass flow, but the exhaust velocity was low compared to a more conventional turbofan with the same thrust rating, so the Harrier was limited to subsonic flight.
Because the JSF was intended to be supersonic, it required a main engine with a high exhaust velocity, but the dry thrust is insufficient to support the aircraft mass in the hover. Another source of thrust is required nearer the forward end of the airframe, hence the lift fan system and its various doors behind the cockpit on the F-35B.
https://en.wikipedia.org/wiki/Rolls-Royce_LiftSystem