At least 12 people are understood to have died following the two latest tremors, according to the Associated Press.
A deep magnitude 6.3 quake on Sunday morning (August 19) was followed by a shallower magnitude 7.0 event, the US Geological Survey said.
The first struck near the north eastern town of Belanting and the second off the coast affecting nearby Sumbawa island.
The disaster is the latest in a series of violent seismic events on the Pacific Ring of Fire.
Hundreds have died since the first serious magnitude 6.4 quake on July 29, which was followed by hundreds of aftershocks.
As many as 500 tourists became trapped on Mount Rinjani following the first earthquake, and in total, it is believed some 2,000 tourists in total have been evacuated.
Lombok is situated east of the more well known holiday island of Bali, one of a chain of popular island destinations east of Indonesia’s most populous island of Java.
The Foreign Office is continuing to advise against all but essential travel to northern areas of Lombok where the seismic activity has been greatest, including the nearby Gili Islands.
“There has been a series of earthquakes and aftershocks to the north-east of the island of Lombok since July 29,” said the FCO.
“These have resulted in casualties and damage to buildings and infrastructure, most severely in northern and western areas of Lombok.
“If you’re in these areas, you should exercise caution, stay away from collapsed buildings, liaise with your travel company/accommodation provider, and follow the advice of the local authorities.
“Where possible, keep your family and friends up to date with your situation and itinerary.”
The FCO adds in respect of the risks posed by further seismic activity: “Aftershocks have occurred, including some of a significant scale.
“These may continue in the region in the coming days and weeks. Risks may be especially elevated in the Gili Islands and areas of northern Lombok closest to the epicentre. Landslides could occur, including in the Mount Rinjani National Park.”
The main airports on Lombok and Bali are operating normally.