If all you have is lump and chips, your biggest problem is going to be keeping the wood smoldering long enough to give a consistent smoke for a longer period of time.
What may work for you right now, given the equipment you have, is this, get a minimum amount of lump going(1 or 2 pieces), then set a bunch of the chips laid out like a snake, on a tray with the burning lump on one end. Stick this on the charcoal grate, or perhaps get rid of the grate and stick it at the bottom of the bowl. Then once the snake is going put the cheese on a rack on top of the cooking grate and let it smoke. Keep the lid vent wide open, but close 2 of the three bowl vents, and use one to provide just enough air to keep the wood going.
I hope this makes sense. In my head I know exactly what I'm talking about, but I'm not sure if I'm conveying it properly.