There are some production class bikes that run fast speeds without a lot of trail. They pay a lot of attention to the things mentioned in the previous post. They also spend a lot of time on the basics like making sure the steering head bearings are not tight, notchy, or loose, the wheels are in near perfect alignment, and the wheel bearings are in good condition. The salt is not always smooth. Rear dampers, if suspension is used, should give adequate damping.
One thing to pay attention to are the rims and tires. The rims should be true. Then mount the tires on the rims and make sure the beads are properly seated and the tires are inflated to the correct pressure. Check the tires to make sure they are true. If not, put on another tire until you get some that are true. Also, if a tire takes a lot of weight to balance it, it is not good for LSR. Sometimes, with certain brands, two or the three tires need to be fitted to get a good one. The Metzelers we run are almost always true and often require no weights to be in balance. This is common for premium tires from some of the other major brands, too.
"True" is a subjective term. Usually I try for less than 5 mm tire runout.