Quick answer: The best time to visit Lisbon is May–June or September–October (warm, fewer crowds). Expect a mid-range budget of about €90 per day. Visa: Schengen area — 90 days in any 180 for non-EU; watch your 90/180 balance.
Why this window
Lisbon is hilly and walkable but the trams and viewpoints reward a neighborhood-clustered plan. Four days covers Alfama, Belém, Bairro Alto and a Sintra day trip without backtracking.