The crows that are digging up your lawn are usually in search of worms or other food that they can eat and eventually if the crows no longer find any worms or food in your lawn then they'll avoid the lawn in the future.
However you could put motion detected sprinklers in the areas where the crows are digging and when the crows get near the motion sensors the sprinklers will turn on and scare the crows away.
Or you can also spread some castor oil granules or beneficial nematodes over your lawn to keep the crows away as the crows hate the castor oil granules and the nematodes so they'll avoid your lawn and avoid digging up your lawn.
You can also spread some pesticides over your lawn to kill off the bugs that are in your lawn which is usually what the crows are after.