I presume that you require to arrive at Seville Airport at 09:00 am SPANISH TIME.(i.e. one hour ahead of Portugal time).
Allowing for the fact that Seville rush hour traffic can be heavy and that the airport in on the North Side of the City, I would allow between 3,5 to 4 hours travel time. You may get a clear run through, but I have been caught in Seville rush hour. It is not nice! Its better to have to kill half an hour at Seville Airport than
I would therefore suggest leaving Lagos between 04:00 and 04:30 a.m.(Portuguese Time)