it is possible that the amplifier has an influence on how quickly the coil leaves the magnet?
Yes and no.
Every amplifier has an output impedance.
Clear has a resonance in the bass area (around 55 ish Hz).
A high output impedance results in the resonance being more pronounced, ie: these frequencies will be played louder. This is the common effect that audiophiles describe as "amp matching" because the result will be a "warmer" sonic signature.
So if you compare a high output impedance amp to a low output impedance one, the "clipping" (driver hitting maximum allowed excursion) will occur earlier on the one with higher output impedance. For me: on my AVR it was much easier to hit Xmax compared to my RME, where the treble would kill my ears long before the bass got loud enough. :'D
Amp vs. amp with the same output impedance should not make any difference.
That being said: the A90 most likely has a lower output impedance than the Lyr (IIRC, it's a tube based amp), so this cannot be explained that way.
As Solderdude already stated: Unit to unit variation in regards to the "clipping" is pretty extreme in Focals lineup. So it might be that.