For folks with very sandy soil, lime can move very quickly. Some folks I know need to apply 3 tons each time they plant. For guys like me with heavy clay, the best time to apply lime was a year ago. You can speed up getting the pH adjustment to root level by tilling in the lime, but you cause other soil damage when you do that. The cost of the short-term gain is burning OM and disrupting soil tilth baking long-term nutrient cycling more challenging. So, anytime my soil tests show I need a half ton of lime, I surface broadcast it. The upside of the heavy clay soils is that lime moves so slowly that once an initial pH adjustment is made, it can be a number of years before maintenance lime is required.
Thanks,
Jack