I dont think its super critical, all these lubes probably would work fine. There were some TS owners that were still on the original castrol after like 40k miles or something with no issues. In fact, I dont think I've heard of a single issue ever with a Lysholm blower, regardless of lube used.
I can't say why ESS originally recommended Castrol. Maybe later they switched to the vortech oil that is used in their normal vortech kits thinking it would be just as good and maybe because vortech used it that it was a more supercharger-specific lube? I'm just guessing.
Like motor oil, I like to use what the manufacturer recommends. So I called Lysholm who actually created the blower itself, and they said they spec the Nye oil. So that's what I go with (or the GM or Ford part number versions of the exact same lube).