What is the going rate for a taxi from Lisbon's airport to the city? And do they take only cash?
We suggest the Metro to most travelers. Buy a Via Viagem card before boarding. Here's the taxi info from the new edition of Rick Steves' Portugal:
Getting to and from the airport is a snap. Figure on 20 to 30 minutes by taxi, Uber, or bus (depending on traffic) or 30 to 40 minutes by Metro. By Taxi or Uber: Taxis line up on the curb at the airport, but are notoriously aggressive in gouging arriving travelers. You’re more likely to get a fair price--and skip any line--by going upstairs to the departures curb and hopping into a cab as it drops off its riders. Better yet, request a ride using Uber. Either way, a ride to or from town should cost no more than €10 to the center. If taking a taxi, insist on using the meter--it should start at around €4 and be set to Tarifa 1 (or Tarifa 2 for nights, weekends, and holidays). There is no “airport fee” supplement, but there is a legitimate €1.60 fee for your luggage (not per bag).
To return to the airport from downtown, simply use Uber or hail a cab on the street. Skip the outrageously overpriced "taxi vouchers" sold by the airport TI--these are for rides outside the center and more than double your cost.
See also this recent report from a traveler who didn't get the best rates: https://community.ricksteves.com/travel-forum/tourist-scams/lisbon-taxi-drivers.
I would plan to get cash from an airport ATM.
We have caught taxis from the airport, it is much faster to go the the departures level. Price was 11 euros from airport to Alfama area.