The report stated they overflew three suitable airports in an effort to get to Lagos.
It is my understanding that this was the last flight of the Captain before he was due to fly back home on rotational leave. If that was the case, then having flown for a carrier in Nigeria for many years, I can understand the need to 'get home' to LOS. However I, like the majority of professionals I have flown with, would prioritise the safe operation of the aircraft above all else.
I would always read all appropriate checklists as a start. However on a twin jet all Pilots know that with an engine problem 'land at the nearest suitable airport' is a given before you even start reading the checklist.
Personally after the first engine issues I would have started a turn back to ABV whilst calling for the appropriate checklist.