I heard mention of it occasionally, but that was also years after the initial move from Digg, so I can't comment on what it was like first hand during the initial move time.
However, I don't think anyone viewed Reddit as a "spite site" for Digg, Reddit was around for years and was semi-popular before Digg committed suicide. It was simply the natural move.
Lemmy on the other hand has been around for a little bit, since 2019 as far as I can tell, but a rather minimal userbase.
Certainly if we get to the point where Lemmy (and its current userbase at minimum) sticks around for a few more years, it'll likely largely move past the whole Reddit fiasco. But it also needs a large variety of non-reddit-related content to interest users, otherwise this site will likely die before it gets there.