At the assessment, the lameness is identified to one limb (usually the left!), but when that limb is blocked out, often the horse shows lameness on the right limb. In other words, both are causing problems, but one is worse than the other, and the worse limb is therefore the one that shows up the problem first.
The interesting thing is that most horses have the left front limb as the worse limb, and if they have a hind limb problem as well (as many do), then the right hind limb is worse.
Of course, there are always exceptions, but all except one of the horses in Project Dexter (and as far as I can remember, all the horses who pre-dated the research), had a worse left than right limb, both in terms of assessed lameness and conformation.