How to reach Lagos:
Follow the N251 in direction of Lagos, or take the toll road exit Odiaxiere and drive to the parking garage Parque da Frente Ribeirinha at Av. dos Descobrimentos, 8600-688.
The nearest airport is Faro airport. Look on googleflights.com for direct and cheap flights. Or visit the websites of your airlines. Transavia, Easyjet, Brussels Airlines, Wizz Air and Ryanair for instance fly directly to Faro.
From Faro you can take a train to Lagos or go with bus (2 euro) to the centre and train-station of Faro and then take the train to Lagos (7,50 euro single price).
Taxi from Faro airport to Lagos is expensive because of the distance (100 km), the one hour drive, high petrol prices and toll road. Prices are negotiable with some taxi, Yellow Fish or Uber-drivers between 95-140 euro. Suggestion: try to combine this transport with other players.
Flying direct to Lisbon is sometimes a cheap alternative. From the Airport take the direct train to Tunes and then to Lagos. From Lisbon there is a Flixbus (9 euro if you make reservation on the internet), this one is leaving from subwaystation Oriente and direct to Lagos.
You can rent a car for a week on Faro airport. But renting a car when needed on daily base in Lagos is cheaper: https://dailyrent.pt/