The powerful quake, whose epicentre was at a depth of seven kilometres (four miles), hit at 6:47 am local time (2247 GMT Saturday), the United States Geological Survey said.
Lombok in southeastern Indonesia is a popular tourist destination, and lies around 100 km east of the resort island of Bali.
The quake struck 50 km (30 miles) northeast of Lombok's main city Mataram, the USGS said, far from the main tourist spots on the south and west of the island.
"One person died in East Lombok and two died in North Lombok," Sutopo Purwo Nugroho, a spokesman for Indonesia's disaster mitigation agency, said in a statement.
No details were provided on how the victims died.
At least two dozen others were injured in the earthquake, and one house was badly damaged in North Lombok.
Island authorities have temporarily closed the hiking trails on Mount Rinjani amid fears of landslides after the quake, Nugroho said.
No tsunami alert was issued, said Hary Tirto Djatmiko, spokesman for Indonesia's geophysics and meteorology agency, but more than more than 40 aftershocks were recorded.
People living near the epicentre said they felt a strong jolt.
"The earthquake was very strong... and everybody in my house panicked, we all ran outside," said Zulkifli, a resident of North Lombok, close to the epicentre.
"All my neighbours also ran outside and the electricity was suddenly cut off," he told AFP.
Indonesia, an archipelago of thousands of islands, sits on the so-called Pacific Ring of Fire, a seismic activity hotspot.
It is frequently hit by quakes, most of them harmless. However, the region remains acutely alert to tremors that might trigger tsunamis.
In 2004, a tsunami triggered by a magnitude 9.3 undersea earthquake off the coast of Sumatra, in western Indonesia, killed 220,000 people in countries around the Indian Ocean, including 168,000 in Indonesia.
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