I'd image the lazy way is to fill the low parts with compost, chuck the lawn seeds of the type you need on it (hard wearing, dry resistant, whatever...) and then let that take root. Keep an eye on it to ensure the compost stays moist so it doesn't get blown away and that the seeds take.
But I am no lawn expert, so see what others say, this is more the "levelling a floor" approach to lawns ;)
I'd image the lazy way is to fill the low parts with compost, chuck the lawn seeds of the type you need on it (hard wearing, dry resistant, whatever...) and then let that take root. Keep an eye on it to ensure the compost stays moist so it doesn't get blown away and that the seeds take.
But I am no lawn expert, so see what others say, this is more the "levelling a floor" approach to lawns ;)