how to get to Lagos airport on public transport

This is how I did it. Note that I took this trip during afternoon rush hour, so the fares could be slightly cheaper during less busy times.

From the Obalende Motor Park on Lagos Island take an Oshudi bound minibus. Note that there are 2 routes to Oshudi - up & down, wait for the Oshudi up minibus as it follows a shorter and more direct path. If you carry a big rucksack (like I did) or have lots of luggage, you have to be patient and wait for a bus that has room in the back for luggage, most minibuses don't have. In rush hour this leg of the journey cost me N150 (N100 for a seat and N50 for the luggage). If you take a minibus without room for your luggage, you will have to pay for 2 seats.

Once you get dropped off at Oshudi, where there are other waiting buses, immediately get on one that goes to Nacu. This one cost me N70.

You will be dropped off right at a taxi park, as long as you mention that you are going to the airport. These shared taxis have 2 destinations - domestic terminal or international terminal. Wait for the taxi to fill up, and it cost me N50 to the international terminal.