I've driven exige on track but haven't ever autocrossed once in my life, but go out on limb to say... the lotus is not a good slow cornering car, in my experience MR cars don't turn unless the balance of weight is brought to frontside, and that is usually achieved with speeds then braking...
widening front track helps. or just max out toe out, camber frontside, and toe in rear side
... jk
the tires that come with the car are special ad048 for lotus, forget the name. but ad048 comes in many other compounds. Not sure if it's available for overseas markets but S compound for soft is better than the lotus standard ones. with time ad050 will come out with the 17 size and we can try that as well.