Flight directly from Singapore
Silk Air flight directly from Singapore to Mataram three times a week. See Www.SilkAir.Com
Flight to Bali, then to Mataram
There are many international flight from Singapore head to Bali. Check your favorite airline company.
Fast boat takes transfer time about 1.5 hours directly from Bali east harbors to Lombok and Gilis island. Free pickup and transfer from your hotel in certain areas. Check Www.GiliTransfers.Com
Public ferry is more cheaper (but needs much longer transfer time) than fast boat and suitable for tight budget travelers.