I've seen your profile picture somewhere before? But I can't for the life of me think where?
Anyway. First off, a Lacie monitor is by far the worst choice of a first monitor. They get very big, need a lot of space, eat a tone, are harder then most monitors to keep and if you get a bite (even a small bite), you'll more then likely end up in the hospital getting stiches.
Now, lacies NEED a very hot basking site, otherwise they can go off food and even cause more serious problems. For hatchlings, 45-55c is a good range, for bigger monitors, 55-65c is a good range (don't worry if it gets hotter then that). But bigger monitors need the basking spot spread out over their body (this is done by using multiple heat lights next to each other).
Do not keep it on sand! Lacie's need a deep moisture holding substrate. Like coco-peat, leaf litter, "kritters crumble", etc. When lacies want more moisture, they will dig down into the bedding.
As well as the basking spot, The proper diet is extremely important. Lacie's should be fed on nothing else but whole bodied small animals, e.g. Rats, mice quails, chickens, etc. meat itself, is not a good diet for a Lacie, because lacie's get their main vitamins from the organs in those animals, not the meat.
I had a Lacie that had metabolic bone disease, due to the previous owner feeding her nothing but chicken breast and the occasional mouse (1 every 2 weeks). Her nose had bent straight down and she couldn't eat on her own.
Here is a link to her thread.
http://www.aussiepythons.com/forum/general-reptile-discussion-42/lace-monitor-mbd-graphic-169275/
Unfortunately, she past away a little while ago, due to organ failure, because her MBD was so severe, it had caused permanent damage to her organs.
Also, you don't want to forcefully handle your Lacie, they are naturally curious and will come to you if given time. This way you will have a Lacie that trusts you and allows you to handle it.
Another reason why it might not want to eat, is if it doesn't have suitable hiding options. Young lacie's need multiple hides and you should NEVER forcefully remove it from its hide (you're trying to build trust after all). A young Lacie should be able to move from one end of it's enclosure, to the other end, without being too exposed. You may not see it for 6 months, but once it starts hanging out (without hiding) while you're around, you know it's not seeing you as a threat.
Good luck, you'll need it.