This is VERY odd.
They (L&M...or whoever) must use very low rated Lithium cells and during use the discharge current must be near the max for them to have such a short cycle life. Lithium cells will fail much faster if they are discharged at a rate nearing the max.
Heatstroke, the link you gave is not standard use - it would be a test in a perfect environment and probably done by the manufacturer - im familiar with those types of pages from Gold Peak (their cells have been, generally, superior to other brands e.g. energizer, etc) cells, each different model of cell has its own test page from the manufacturer.
Its also done at an extremely low current, 0.2C would take 5 hours to discharge at that rate. Im not familiar with lights, but they have to drain the cell much faster than that, correct?
RC Hobby cells are usually more robust than most, but they should follow the same life cycle pattern, etc, that most other cells do. Keep in mind im more familiar with Li-Poly than Li-Ion.
Given their cycle-life I'd go with the NiMH, but usually the Lithium would be far better - im suprised by the info you guys posted.