From Melbourne, follow the M1 to Geelong and then take the Great Ocean Road to Lorne. This will take just under 2 hours, however, allow a little extra time to stop along the way as there are plenty of opportunities to admire the breathtaking views. You can save a bit of time by travelling inland from Geelong to Winchelsea and then taking the C151 to Lorne, however, this is nowhere near as picturesque or iconic as the Great Ocean Road.
Geelong is only 19 km from Avalon Airport, and only a $30 taxi fare. There are also bus services from Avalon Airport to Geelong that operate in line with flight arrivals.
If you are wanting to take public transport to Lorne, there is a Vline train that runs from Melbourne to Geelong. Trains depart from Southern Cross Station and there is a train at least every hour, and takes just under an hour. From Geelong train station you can take a bus to Lorne. The buses are operated by Vline and there are about 4 services a day, with more in summer. The trip from Geelong to Lorne will take an hour and a half. The combined fare from Melbourne to Lorne is $19.40. You will be dropped off at the Lorne Pub.
If you want to check out Lorne but have limited time then Tours to Go offers a day trip from Melbourne to the Great Ocean Road. Departing Melbourne at 8am and returning at 7.30pm the tour takes in the major sites along the Great Ocean Road with a stop in Lorne, Apollo Bay and Otway National Park. It is $165 for an adult and this includes morning tea.
Once in Lorne there is no public transport, only a taxi service, so if you choose to arrive by public transport it may be best to stay in the heart of Lorne for easy access to the beaches and cafes.