Traction control can be added with a BOE/Kold Fire tune an traction control button. You will need that with the factory LSD to stay in stock class.
You definitely want the LSD for auto-x but you could still have fun without it. You just will not be as fast and will have to deal with wheel spin accelerating out of the tight corners.
It's my guess that the lsd is worth somewhere around .3 to .7 seconds on an elise with a stock power output (for a course that SS class would run at about 50 seconds). Depends on the course and the driving style. Enough to matter quite a lot for championships, but not so much that you MUST do it right away if you are just running for fun locally. There will be an occasional course where you really wish you had it and it may cost you a second or more, but slaloms and transitional stuff won't care too much as long as you have the stiff front bar.
The elise is regularly in the SS trophies for nats
Now if one bumps up to SSP (formerly ASP) one generally does an Option conversion (including super charger) to become an Exige. Really better to just start with an exige here.
or for SSM Weight becomes an issue. The car is too light by rule with boost so one either Adds Huge boost and 150lbs of lead up to 2120lbs or replaces pistons/valves/crank/oil system/etc etc etc $$$ etc etc and oh yeah more $$$, stroke and revs it over 9k and shaves weight down to 1805lbs. Most competitive street modified engines are ticking time bombs. I know one national competitor that has had 3 engines in the last 3 years.
And then there's XP where the franken lotus that was an elise has won 4 of the last 5 years. XP is probably more $$ still, but less headache with rules.
SS and XP are arguably the sweet spots. Stay stock unless you have another $15k-$30k to pour into the car, or you don't really care much about winning. (Do as I say not as I do
As the power goes up the LSD will matter more. But for stock cars it can wait until you are within 1-2 seconds of someone who is nationally competitive.