Lamia is a compact city and the main sights are walkable from the centre. The castle hill is a 15-minute walk uphill from Plateia Diakos, the central square. Taxis are cheap and readily available.
For Thermopylae, you need a car or the local bus heading south on the E75. The hot springs and Leonidas monument are a few kilometres apart along the main road and are not easy to reach on foot from each other. Most travellers hire a car or take a taxi from Lamia for the half-day.