The town centre — the main bazaar street, the railway station, the bus stand — is compact and walkable. Everything else requires transport.
Auto-rickshaws are the default for shorter hops: Bhushi Dam, Lonavala Lake, and a few of the nearer viewpoints are reachable by auto for a fixed fare. Negotiate before you get in; meters are rarely used.
Hired cars and taxis are essential for the more distant sights: Karla and Bhaja caves (10 km out), Tiger's Leap (12 km), and the Lohagad fort base are not practical by auto. Local taxi operators outside the railway station offer half-day and full-day rates that cover the main circuit of sights. If you're staying at a resort, the hotel can usually arrange a vehicle. App-based cabs (Ola, Uber) have coverage in and around Lonavala but availability is inconsistent outside peak hours.
Two-wheelers (scooters and motorcycles) are available for rent from a few outlets near the station and main road. Rates are reasonable. The roads out to the viewpoints and caves are manageable on a scooter and allow you to stop wherever you like, which makes them a good option for independent travellers comfortable riding in India. The Bhushi Dam road on a monsoon weekend is congested; allow extra time.
On foot: the main street is the only stretch of Lonavala genuinely suited to walking. The road out to the sights has limited footpaths and moving traffic.