Baixa, Praça do Comércio, Alfama lanes, the castle or one viewpoint, Chiado and a relaxed dinner.
Day 2
Belém & design
Jerónimos timed entry, Pastéis de Belém, the riverfront, then MAAT or MAC/CCB.
Day 3
Culture & local life
Gulbenkian/CAM or MUDE, Príncipe Real, Estrela and Campo de Ourique.
Day 4
Day trip
Sintra for palaces and forest, or Cascais/Caparica for an easier sea day.
Day 5+
Go deeper
Évora, Ericeira or Arrábida; add markets, a second museum day and slower evenings.
Honest thought: September rewards flexibility. Keep exposed sights for the cooler morning, hold one day open for the best beach weather, and bring a light layer for breezy evenings.