It isn't coming out of nowhere, for light speed perceptions we use 1 m / speed of light, 1 m is an arbitrary accepted value, I did the same here but replace light with lightning.
No it isn't. No official page states that value so it isn't officially accepted for general use. When in doubt, both calcs can be wrong.
I mean, really, the entire scaling form character stats thing is always dubious. For a technique that turns you into real-life lightning to be always lightning speed is one thing. It's a technique, so it makes sense for it to always have the same speed. But otherwise characters don't make consistent use of their stats. A character stated to be supersonic isn't moving supersonic 100% of the time. Similarly, reactions of characters aren't constant. If characters, like in this case, get surprised by something they of course react slower.
The calc in question here doesn't even qualify for overcoming perception. To quote: "Witnessing these movements, which could be described as beautiful, most of those present weren't able to respond immediately."
It literally said they could in fact perceive the movements, which would mean they weren't below their perception time.
Anyways, what the more general case is concerned ask yourself this: What does "lightning speed reactions" or "lightspeed reactions" mean? Like, assuming the fictions actually stated that in particular. We might have our definition of what that means, but that is a vsbattles terms. It obviously doesn't apply to authors. That's the difference to something like a lightning speed statement. Lightning is a real-life thing with a real-life speed. That term is unambiguous. The same doesn't go for the reactions statements, as they have no universal definition. An author might have a different idea of which timeframe it should refer to (or if it even refers to a timeframe and not something like a speed value).
Other option is to say: "Well, they have lightning speed and can manoeuvre, so they need lightning perception".
The reasoning isn't wrong, but it is a calc. It is basically the same as this theoretical case from the calc stacking page:
This usually occurs if a feat is quantified per a rule of thumb instead of precisely calculated. A typical example would be a character dodging a bullet from a short distance being ranked as "Supersonic" and then using that ranking to calculate the speed of another character, whose speed one can compare to the former in some feat.
While it is acceptable to rank a character by such a self-evident feat without a calculation, one should keep in mind that the unwritten calculation is only skipped due to being trivial, but is still the justification for the ranking. Hence calc stacking will still be an issue for such feats.
One could say the character has "bullet dodging speed", but to determine what that actually means in numbers a calculation would be needed.
If you want to get a perception timeframe from a character manoeuvring at x speed, you need to see a case of them doing so and find a fitting distance to use.
We had a thread some time ago about reactions of characters flying through space, for example, were we determined that their perception time is at times much lower than their speed due to the massive distances involved in space travel.
In short: We usually skip the calculation for the perception time of a character as it's clear they can react at their combat speed, but if you want to use a particular number a calculation is necessary.