"Slow" is not the way I would describe his playing on Seasons in the Abyss or Silent Scream at all.
I know his style wasn't all about speed, I'm generalizing a bit. But whenever you hear anyone in the metal scene praise Lombardo, it almost always, 99% of the time comes down to speed. He wasn't known for his grooving or his compositional abilities.
Seasons is a mid paced thrash song. It's midtempo, in no way a fast song. Silent Scream is fast but I don't think it's as fast as Angel of Death or Raining Blood, both of which came earlier. Seasons in the Abyss, Live Undead, Behind the Crooked Cross, Expendable Youth, all slow/midtempo songs he was exceptional in and attracts a lot of attention for his performances there. Same with South of Heaven, another slow song. He's not just double bass, and while the drum community might care a lot about him pushing double bass forward, among your average metal listeners he's noticed for the astonishing creativity and originality of his general style, not his double bass speed which is something only drummers would notice.
Lombardo's versatility is exceptional. Slayer, Grip Inc., Fantomas, all very different and creative bands. Also, from wiki: "In 1999, on his constant quest to expand his horizon as a drummer, Lombardo collaborated with Italian classical musician Lorenzo Arruga to record Vivaldi - The Meeting. The seven-track album had drum improvisations on Vivaldi's work including two pieces from The Four Seasons composition." (http://en.wikipedia.org/wiki/Dave_Lombardo
) Then there's the hip hop instrumental album Drums of Death with DJ Spooky: http://en.wikipedia.org/wiki/Drums_of_Death_(album
). From the Lombardo wiki: "In 2005, Lombardo recorded Drums of Death with DJ Spooky. Spooky played some records, with Lombardo playing along and interpreting his own rhythms. Spooky recorded the session and took the tapes to his New York recording studio, downloaded it onto his computer, and mixed the beats and drums incorporating scratching and other DJ techniques." Then there's his playing with Apocalyptica.
As far as groove goes Sherick I beg to differ. Half of why Lombardo is so unique in thrash metal is his absolutely astounding groove, universes beyond his contemporaries like Ulrich (who I like a lot by the way). From wiki: "As well as considering him an influence, Arch Enemy drummer Daniel Erlandsson feels Lombardo is 'really tasteful in his playing, and doesn't overplay. He's gifted with a groove that not many speed metal, or metal drummers generally, have.'" (Lombardo wiki.) Honestly I must stress again that your average non drummer realizes Lombardo is 'special' because of his fills/accompaniment being totally unique, and his groove, the influence of latin rhythms/style on his sound. He doesn't sound like anyone else in thrash, or even in fast metal period.
I urge CRJ to at least listen to some of the songs I've mentioned here before deciding Dave's place is set. As I see it he takes Aldridge in creativity, originality, skill, and stylistic versatility (which he had a lot of by the way even just within Slayer's 1988-1990 period, not even to mention the other settings he's played in), and ties in influence. He also I think takes Carey in originality, ties him in creativity, and rivals him in stylistic versatility, not to mention the obvious wins in influence and innovation. I think he's being sold short in this discussion of the teen spots we're having and I'm trying to rectify that