Lappeenranta is a city in Finland.
West towards Helsinki
Just on the road in front of one of the entrances to the airport there is a bus stop which is just before it joins to the E-6 highway (exactly here). I think there isn't any bus stopping there, but it is a good place to hitchhike. You will get a lot of the traffic (not people coming from the center though) coming out of the city in direction west, plus the people coming out from the airport.
Other useful info
Ryanair and mainly lowcost companies operates in Lappeenranta airport, so it is quite easy that someone coming from the airport will pick you up and take you to Helsinki. You can also try to go when a flight of your interest lands and go to ask people to give you a ride. There aren't many flights every day, so you better check the flight arrivals from this website beforehand.