Lyft doesn't operate in Europe.

Uber is available in larger cities. But in my experience there are not enough drivers on the app in Frankfurt, wait times are ridiculous, and it's usually not cheaper.

Taxis are the way to go. At FRA just go to a taxi stand. In the city you can either hail one on the street or use an app like FreeNow (formerly MyTaxi) to call for one. It's also a more reliable way to be able to pay with credit card.