To get from Vilnius International Airport to EIGE you can use public transport: Bus fares and schedules
The airport can also be reached by cabs of any of the taxi companies servicing the city. Be aware that the taxis that are already at the airport are known to be 3-4 times more expensive than the ordinary ones. For your information we are providing a list of taxi services in Vilnius that charge reasonable rates:
Tip: Taxi rates are up to 3-4 times cheaper when you call one instead of hailing it the street.