Enjoy a pastel de nata and coffee at Manteigaria (Praça do Comércio) or the historic Confeitaria Nacional; both open ~8:00 and give a classic Lisbon start.
Sample varied Portuguese and international stalls at the market which opens ~10:00 on some days but many counters open earlier; great for a flexible breakfast.
Pharmacia offers playful decor and Portuguese tapas near Bairro Alto; Rio Maravilha atop LX Factory has great skyline views—check opening hours (~19:00).
If Tuesday is a flea market day at Feira da Ladra (usually Tue & Sat mornings), browse antiques; otherwise enjoy a relaxed pastry at a nearby pastelaria (many open from 8:00).