Taxis in Luz and Lagos are quite reasonably priced and can be extremely handy, they are normally beige or black colored and are usually high end cars. The taxis generally have no meters but follow a standard fare table based on mileage. So you can always ask how much to a certain place before starting the ride.
In high season its usually worthwhile to pre-book taxis for longer trips (it will be easier and cheaper). The taxi stop can be found in the center of town, near the bus stop and the Luz church in high season there will normally be a taxi parked there, also most restaurants will order one for you if need.
On low season it is more uncommon to have taxis waiting, so you will need to call for one.
For local taxis or urgent taxi, you can Call Taxiarade (they will come from Lagos to pick you up), no pree-booking for that, just tell them where and how many people, their phone numbers are: 0351 282 460 610 and 0351 967 238 507.
For booking of transfers to and from the airport you can use Luz Serviços e-mail: firstname.lastname@example.org and telefone number: 0351 282 788 522, they might have more flexible airport transfers and airport taxis that they can book for you.