It is not difficult to produce thin Li-ion cells less than 2mm thick. However, it would be useless to you if we sent you a cell that cannot perform according to your requirements. So, please provide the following information first, and then we can tell you if we can provide you with a 2mm or thinner Li-ion cell:
Max continuous discharge current
Peak discharge current/for how long
Max continuous charge current
Operating environmental temperature (max high & low)
Preferred physical dimensions in width and length or in other irregular shapes
Annual quantity (this would help if you want the cell at the lowest price)
A friend in China who produces thin cells just told me they can produce cells as thin as 0.5 mm. They currently produce 23 cell sizes from 0.5 to 1.5 mm thick.