I'm with MT in that I think you'll be ok as the camping season hasn't' officially opened yet, that's next weekend.I kinda have my hands full right now with race stuff but I'll try to at least make some calls tomorrow and see what it'll take to hold a spot. Will you be tenting? Really, this early I don't think there's a big danger of Liberty Lake filling. It's lesser known as a camping destination (but a perfectly pleasant spot).
here's reservation info for STATE parks,(Riverside, has showers)
http://www.parks.wa.gov/reserve.asp
Liberty Lake, scroll to bottom,
http://www.spokanecounty.org/parks/parklisting.htm
first come first serve, no reservations.