A few pair of swans for the lake make a beautiful sight, don’t tear of up lawns and make a mess, but keep the geese away!
The easiest way to get rid of the geese is to stop mowing grass in a narrow perimeter around the lake. If the geese don’t have a clear line of sight to spot predators, they leave.
I’ve done this for years with a quarter acre pond. I bale hay in the surrounding field. Around the pond, I cut nothing. I’ve had geese come in at dusk. Come morning they scoot.