For Li primary CR2 performance, see
this thread. Scroll to the 3rd graph in post #1. It looks like the tested cell can hold 2.5V at a current draw of 0.5A to 0.75A. If you use 1xCR2 to power a boost driver,
driver efficiency * Vbatt * Ibatt = Vf * If
If we assume a driver efficiency of 80%, then we can deliver 0.8 * 2.5 * 0.75 = 1.5W power to the LED. If efficiency is 90%, then the power increases to 1.69W. If Ibatt is 0.5A, then the power delivered might range from 1.0W to 1.1W.
If you look at the XP-G datasheet, the typical Vf at 350mA is 3.0V (I've measured 3.2V at ~1000mA, so certainly Vf can be a lot lower than the typical datasheet value, which would really help when using 1xCR2).
0.350A * 3.0V = 1.05W
Thus, 1xCR2 should be able to power an XP-G at 350mA drive current even for a driver with an average efficiency of 80% and assuming that the CR2 can hold 2.5V at 0.5A current draw.
If the cell can really hold 2.5V at 0.75A and deliver 1.5W, then looking at the XP-G If-Vf graph in the datasheet, the If-Vf pair that gives 1.5W is about 500mA/3.1V. Thus, it might be possible to drive the XP-G at 500mA.
If driver efficiency is better than 80%, then you can deliver that much more drive current to the LED, but to be conservative I'd say that a 500mA boost driver is about the max you can reasonably expect. A 350mA driver is looks well-within the CR2's performance envelope.
At 350mA, an XP-G R4 is rated at a min of 130 emitter lumens. At 500mA, an R4 looks like it can deliver about 180 emitter lumens.