The island attracts tourists from around the world due to its beaches and hiking trails, and is located about 40km (25 miles) east of Bali.
More than 160 people are injured and thousands of homes are damaged, officials say.
A Malaysian tourist who was on a hiking trip to Mount Rinjani is among those killed.
The US Geological Survey said the epicentre of the earthquake was 50km (31 miles) north-east of the city of Mataram, in northern Lombok.
It was followed by more than 60 smaller earthquakes, with the largest recorded at a magnitude of 5.7.
Mount Rinjani National Park, a popular destination for trekkers, has been closed due to landslides.
Indonesia is prone to earthquakes because it lies on the Ring of Fire – the line of frequent quakes and volcanic eruptions that circles virtually the entire Pacific rim.
More than half of the world’s active volcanoes above sea level are part of the ring.
A magnitude 6.5 quake struck off the north-east coast of Sumatra island in 2016, killing dozens of people and displacing more than 40,000, reports BBC.