Unless you are definitely sure that your health coverage at home will cover you in Bali and Lombok, you should take out travel insurance; bring a copy of the policy as evidence that you're covered. It's a good idea to get a policy that pays for medical evacuation if necessary.
Some policies specifically exclude 'dangerous activities,' which can include scuba diving, renting a local motorcycle and even trekking. Be aware that a locally acquired motorcycle licence isn't valid under some policies.
Worldwide travel insurance is available at www.lonelyplanet.com/bookings. You can buy, extend and claim online anytime – even if you're already on the road.