Try the terrace car park. It's an overflow for the Civic Centre, and is free at the weekend (most of the other car parks are 50ph or limited). Then walk across a couple of bridges and you'll be at the east stand of the stadium.
Ignore the 2hr limit the link says, you can stay there all day if you want.
https://en.parkopedia.co.uk/parking/carpark/terrace/eh54/livingston/?arriving=202207261600&leaving=202207261800