My husband and I spent a week in Lisbon in 2011. Our apartment was in the Alfama area. About 3 blocks from it was Sr. Fado. It's very small and intimate. We had dinner and stayed for the performance. Reservations were required and they didn't perform every night. Here's the link:
https://www.sr-fado.com/
There's public transportation down the hill at the train station. It was so late when it was over that the owners offered to call us a cab to get home. They were surprised that we declined and told them that we were staying so nearby.
We went to another performance in a larger, more touristy place near downtown. We didn't enjoy it nearly as much, but they did have a good rabbit meal.
It's been 10 years since we were there, so things may have changed, but the Sr. Fado website looks pretty much the same.