I've been lurking on this forum and have researched your question to a sickening degree.
Yes, LSD was an option in late 2005 and delivered on 50 cars thus making it SCCA Super Stock class (SS) legal. In every instance LSD includes traction control (TC) with the TC switch positioned very close to the shifter which may be accidently triggered by your knee during spirited driving. A solution for this is to cover it with a plastic bottle cap and tape.
LSD is a stand-alone option costing about $2,000 from the factory. There are no other prerequisites meaning you may find LSD on a non-sport and/or non track-package car.
As far as the best SCCA platform to start with I believe the recommendation would be for a 2006 Elise with Sport Package (wider front wheels and twin oil coolers), Track Package (adjustable suspension, adjustable front anti-sway bar, rear suspension brace, harness bar), and LSD. Touring Package has no benefit or detriment for racing and technically you could probably do without the hard top as well.
Finally, as a serious competitor yes you do want LSD as there is no other way to eliminate inside rear wheel spin coming out of tight turns. You can and I myself hope to be competitive without it but we're not going to win nationals without it.
They are a rare find but not impossible. See this post and I believe this car was recently on Ebay:
Good luck in your search!
[FONT="Verdana"][SIZE="2"]2005 Elise Ardent Red / Biscuit Leather / Touring / Hard Top / Converted to LSS / Larini "Sports" Exhaust System. No Star Shield