This is how I get to Lekki from unilag.
From Unilag gate, cross the road to the other side and take keke going to Unilag junction. This costs about 200 Naira.
Once you get to the junction, cross the road to the other side, where you'll see danfo buses going to Obalende. Also, if it's not rush hour, you might have to wait a bit until the bus fully loads.
From the junction to Obalende is about 500 Naira, but if it rains, the price may fluctuate. Immediately you get to Obalende, you'll see buses going to Lekki and Ajah. Know that it's quite pricey, so about 1,200 Naira. Sometimes up to about 1,500 Naira. It is quite overpriced.
Once you get to the bus stop, you can take a short walk if your destination is close to where the buses drop you off. If you get lost at any point in time, you can always ask someone for directions.