It's an interesting question if the USMC had been told that a Supersonic Stealthy STOVL jet was not worth the candle, would JSF have been a twin engine aircraft?
Given the convoluted history of several programs being merged into the JSF program, I think the stage was pretty much set for a single engine. Yes, VSTOL mas a major driver for the single engine design, but so did risk, weight and cost. A precursor to JSF was CAST, a common "affordable" platform with a single 119 derivative engine part of the mix from early on.
One requirement that seemed to carry from the CAST to the JSF program was the max weight of 24,000 lbs- the max a single 119 derivative was forcasted to lift.
DARPA / Navy Common Affordable Lightweight Fighter (CALF) 1993-1994