The dust from the lime can irritate the sensitive tissues, eyes, nose and mouth. If the pasture is lightly limed we just left the cows on it, if heavily limed we wait until a rain or a cople of heavy dews to wash off the grass.
Considering your location, are the cows still grazing the grass or just on it? You can do a split application. Lime 40 acres, and leave the other hald alone for about a week. This may or may not help if the cows get curious, but if you could run a strand of electric across, it would keep them from inhaling it. Also, you can have the liming timed to be put one a day or so before a shower. Wouldn't have to be much, just enough to get the dust settled off the leaves.