One mother Helen Milne told the BBC that her daughter, Laura, from Oxfordshire, is on Gili T. She said: 'They are stuck on the island and are reporting rioting, fighting, and people can't get on boats.
At least91people were killed when a 6.9-magnitude natural disaster and strong aftershocks rocked Indonesia's resort islands of Bali and Lombok on Sunday, causing people to rush out of homes, hotels and restaurants.
Sunday's quake came a week after another that hit east Lombok, killing 12 people. The sources said that the quake on Sunday evening was the main shock while the smaller one on July 29 was the "foreshock".
The epicentre of the quake was the northern slope of Mount Rinjani, near where the previous quake struck a week ago.
Recorded to the north of the tropical island destination, the quake happened around 6.46pm local time.
According to BMKG, there were 20 aftershocks recorded up to 20.40pm local time.More news: Samsung launches Galaxy Note 9 with big screen and Fortnite
The quake also shook neighbouring Bali.
A spokesman for Indonesia's disaster mitigation agency said many buildings had been affected in Lombok's main city of Mataram, a lot of them built with weak construction materials.
He said three ships had evacuated 1,000 tourists so far.
There are now nine New Zealanders registered as being on Lombok.
The Ministry of Foreign Affairs and Trade said New Zealand's Embassy in Jakarta was responding to the quake. The authorities had carried a rescue operation for the trapped tourists in landslides on Mount Rinjani, an active volcano on the Lombok island.
Airports on both Lombok and Bali are both operating normally despite some minor damage - at Bali's Denpasar airport some ceiling panels were shaken loose by the tremors.
It was the second deadly quake in a week to hit Lombok.More news: Harry Redknapp warns Jack Grealish about moving to Spurs
The Indonesian Red Cross said in a Tweet that it helped a woman give birth after the quake at a health post in the north. All but two were killed on Lombok; the others died on Bali.
The worldwide airport of Bali suffered damage to its terminal but the runway was still unaffected and other operations had returned to normal, as reported by disaster agency officials.
Mataram residents described a powerful jolt that sent people fleeing from buildings.
On Gili Trawangan, one of three popular vacation islands near Lombok, thousands of tourists and locals spent the night on a hill fearing a tsunami, said British visitor Saffron Amis. Many buildings had been affected, debris is littering the streets and the power is out in many parts of the main city Mataram.
"Earthquakes as devastating as they are, are really not surprising for Indonesia it's just that they're not widely publicised worldwide, other than if they are in, or close to Bali", he said.
Yesterday Lombok was hit by a 7.0 quake, leaving nearly 100 dead and thousands displaced.More news: Argentine Senate rejects historic abortion law