Taxi drivers at Lisbon Airport are a right bunch!!! Ever since the metro extension opened to the airport, and they have lost trade, they have been out to shyster poor unsuspecting punters.
The local police(PSP) arrested at least airport 20 taxi drivers for malpractice in 2014 according to the local press.
In the past three months, I have had run-ins with two taxi drivers at Lisbon Airport, one who took us on a long new ring road motorway diversion, adding 4km to the trip between the Airport and Praça Saldanha, before I could stop him. The other one took exception to me asking him politely to take us DIRECTLY to our hotel without passing GO and collecting $200.
I should point out that I have known Lisbon for over 40 years, I live in Portugal and I am reaonable fluent in Portuguese!!!!
It should not cost more than 25/30€ one way for the above with bags depending on the time of the week/week-end or day/night and should be considerably less.
What to do if you are a first time visitor to Lisbon??
Consider taking the Metro or Bus if possible! Avoid the Taxi Rank at Departures.
Alternatively, although it may cost a bit more, I would suggest considering buying a pre-paid taxi voucher on-line from the AskmeLisbon website:
This site is operated by the Lisbon Tourism authorities. They have branches at the Airport and in town.
For more info one can call them on : (+351) 210 312810 or contact them via Facebook.
From the map I reckon the trip is located within the 1coroa option but check with the hotel or AskLisbon..
Prices quoted on the AskLisbon site are much cheaper than you have been quoted. You might get charged something cheaper picking up a cab BUT for peace of mind a pre-paid voucher may be a better option.