You'll find free WIFI, but not everywhere.
Cell service should be fine.
As to WiFi, you can find free networks but definitely not everywhere you go in downtown.
Ok great thanks!
I have never had any problem in Lisbon but I have a Portuguese cellphone. Don't forget that if you are using a USA phone the roaming charges can be huge.
McDonald's has free wifi as do many bars, hotels do also.
Free to customers of course. You do have to spend some money. There are few, if any, totally free public wifi services.