Honestly, as I have said before, The Gili Islands is not a great fishing destination. I have spent many many dozens of hours fishing there for little return.
It's also IMHO not a very nice place these days after the massive, uncontrolled development boom over recent years. But maybe that's just me - I fondly remember the laid back, charming nature that these islands used to have.
In the peak periods of the moon cycle, then fishing will be a little better than other times of course, but it is never great.
I would suggest you would have most success with a 20-30 lb set up and fish small stickbaits, metals and even soft plastics.
Yes, there is quality fishing to be had in Lombok but it is a long way from the Gili Islands (about half a day of travelling each way). Here's a simple map showing the relationship - you will see Gilis in the northwest and I have marked up the prime fishing spots in the south. You would need to go down and stay at Kuta Lombok to access the good fishing.
