Since it is an island the most practical way to reach Lombok is by flight from any major international city. Or you can fly to Jakarta and take a cheap domestic flight to Lombok from there.
For Indians the most economical way is to reach Changi airport in Singapore from any major Indian city and then head to the Lombok International Airport from there.
A direct flight can be taken to the Lombok International Airport from most international cities.
Lombok is an island so you can't reach here by cab from another city.
Lombok island does not have railway connectivity with other islands yet.
Lombok island can't be reached by bus from another city.
There are many ferries which operate between Bali and Lombok but they may take up the entire day. Smaller speedboats are available as well but they are more expensive than a direct flight would be. If time is not a point of consideration then you may take a ferry otherwise consider taking a direct flight to Lombok.
Lombok can be covered quite conveniently on bus, taxi, car rental, motorcycle or bicycle too. You can also try the local cidomo which is a horse driven cart, if you are daring enough. This is the main means of transport on gili islands which are vehicle-free.
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