There are several flights from different locations such as Bali, Jakarta, Surabaya en Singapore.
All 4 mentioned airports have an international terminal.
From there, tickets for flights to Lombok can be purchased through several ainlines such as LionAir, Airasia or Garuda. You can also purchase a ticket through a travel agency.
From Bali there is also the option of taking the ferry from Padangbaai. Combination tickets (ferry and bus) with Lombok Sengiggi can be purchased in Bali.