Any problem traveling around Lisbon area only speaking English?
No. Not many people speak Portuguese as a 2nd language so English is quite acceptable and widely spoken.
I’d suggest at least learning to say hello and thank-you. A quick google search will give you the pronunciations.
No issues on our trip. There seems to be somebody everywhere who knows some English. If you know Spanish you’ll be able to read most of the signs since many words are similar.
Zero problems having no Portuguese, especially if you are in the touristy areas. As mentioned earlier, learn a few words - Bom Dia, Boa Tarde, obrigada and obrigado as a courtesy.