I would assume most lameness specialists would be vets (but could possibly be farriers, too, I suppose). So you'd have to go to vet school- which requires a bachelor's degree first. Something like biology would be a good undergraduate major for vet school, and in turn, taking any advanced biology/chemistry/anatomy/life science classes your high school offers would be a good start. I'd stay away from undergraduate majors like 'equine science' as these might not prepare you well for vet school (though you could certainly do that as a 2nd major or minor) Remember that vet school covers all animals- you can't just pick and choose which animals you learn about.
I don't have any figures on what a lameness specialist would make, but I know my own vet told me that equine vets right out of school don't make very much money. However, those that stick with it eventually make a good salary. As a lameness specialist, you'd probably make more than 'regular' equine vet, but you'd have to be a 'regular' vet for a while before you could gain the experience to be a specialist.
Shadowing an equine vet would be good experience, as would volunteering at a horse (or even small animal) rescue. Be sure to let any organization that you decide to volunteer with know that you're considering a career in animal health and that you'd like to get involved with those tasks that involve the vet, etc.
As far as the kind of facility to have, it really depends on what you end up doing. You might join an established practice or university hospital, in which case they would have all the facilities already. You could practice on your own- in that case, you could have as little as a small office to serve as your 'home base' while you do only farm calls (and refer to university hospitals for procedures that require additional equipment), or you could build up a larger facility where clients could come to you and you have some of the specialized equipment on hand.
Pros... you get to work with horses and help them get better. The type of work & lifestyle do have to appeal to you for this job to really have a lot of pros
Cons... equine vets have to do a lot of farm calls, including emergency calls at all hours. When you get to the point of specializing in lameness, you might be able to cut down on those, as you'd have the ability to schedule more appointments ahead of time and leave responding to emergencies to the 'regular' vets. Not all horses are well mannered (and even those that normally are might not be around a vet or when injured), so your chances of getting injured are pretty high. You might find it frustrating when an owner ignores your advice and the horse suffers because of it (this will happen a lot)