Two different amps altogether. I've owned both simultaneously and they both have very different tonal traits. LSS will never get you that chimey, glassy tone. If anything the aC30 can get into the blues tonal world with the right pedal such as the Keeley modified blues driver.
I've got an LSS and had a gold in it briefly (didn't like it - the C90 is actually better for my purposes). It definitely won't do the AC30 "thing" without pedals. That said, it LOVES pedals. I use the Xotic AC plus for AC30 style tones, and the Xotic BB plus for hard rock tones. This amp loves OD pedals - I've also tried hotcake and G2D custom, Jekyll and Hyde, MI Crunchbox and they ALL sounded great through this amp.
I've got an AC30 as well and it's awesome but the LSS is my #1 amp for gigging - it's very versatile, easily moved (mine's a 1x12) and works as a fantastic clean to work with (with pedals). Nothing does the AC30 tone like a real AC30 cranked though.
Yeah, I own both right now and no, the LSS doesn't really do the Vox thing, though they are both EL84 amps. It's emphasis is more low end than high mids like a Vox. I find the clean channel more Fender-y than Vox-y ( and I am using Blues in a 2x12 cab to boot). The dirty channel has more of a Marshall-y thing when pushed. That said, the LSS head gets the gig every time. Versatile, well thought out amps that sound great.