My buddy has a sod farm in Dayton Texas. He recommends cutting up all the grass that way the old grass roots will be out and the new roots don't have to compete with the old root system for space. After its cut out, then you can aerate the soil, put the lime down on it and it can do the PH balancing thing better as its penetrated into the soil. But he says Lime is best applied in the fall or winter and to use the pellets vs granulated as the pellets will stay where you put it. and to make sure you water the lime adequately because it'll help with the reaction.