I recently visited Klaipeda and while my friend was prepared to drive to Kaunas to collect me from the airport, it would have meant her driving two and a half hours each way plus the fuel cost for a 450 km round trip.
For visitors such as I, an alternative is the Airport Express which meets incoming flights at Karmaleva and takes you to the car park at Akropolis in Klaipeda. It takes about two and a half hours and costs only 59 Litas.
Be aware though. The driver is Lithuanian and he may be reading, talking on the mobile phone or, in the case of my recent trip, trying to write while driving.
You can prebook online or purchase a ticket from the driver at the airport. In November there was plenty of room on the bus, in summer perhaps prebooking would be a good idea.