Well for festivals, unfortunately, you are a bit late for Rock in Rio (last week of May) and early for CoolJazzFest (starts in July) or Super Bock Super Rock (End of July)
When you say "local music" do you mean bands from Portugal?
Check out http://www.festivaisverao.com/Agenda/index.html
It has a pretty good listing of events from small shows to festivals
Not much for that week though... over 10 years ago
If you want so listen to traditional music, specially fado, you will have the opportunity for it for sure. In Alfama, the hill where you find Lisbon's castle, there are several restaurants and nice places, where you can eat and listen to fado. The best will be, after arriving, checking with your hostel or in turism, or, in a more adventurous and risky way, go for a walk and find a place yourself.
Around the castle (just ask someone), for drinks at night, you should check: "Chapitô" — school for circus arts, with a theater, restaurant, bars, and concerts, also one of the best views over lisbon. "Bar das Imagens", another nice bar, 200 meters down the street, just a bar. "Terraço" is in front of Bar das Imagens and it's a marvellous and gigantic terrace with chairs, where you can sit, and drink something, with nice music playing. This is probably the best view over lisbon, from this hill.
On the other hill in front of this, you have to check Bairro Alto, the place where everybody goes out in Lisbon, with hundreds of bars, some with live music. And Miradouro de São Pedro de Alcâtara, from where you can see the Castle. At the time when you're here, will have live music some of the nights (probably Thursdays), but for sure has a nice kiosk where you can drink beers and enjoy the ambiance, a really good one.
Well, in July there are lots of things happening around here, ask people when you arrive, nice events happen everyday. over 10 years ago