That chip is a boost converter, which is a very good topology for an LED driver, but it has one big limitation: the LED Vf must be significantly larger than the maximum possible input voltage, otherwise the LEDs are always on (through the diode which you can see on the front page of the datasheet!), and current can't be regulated or limited.
This means, for a li-ion battery with Vin_max=4.2V, the load must be at least two white LEDs in series. If you have just one high-power LED with Vf=2.9V, this won't fly. For larger string of LEDs, this is excellent. Do you have just a single LED, if yes, then look at buck topology LED drivers, and pay attention to the minimum voltage drop-out (you would want to use the battery down to, say, 3.2V, and if the LED requires 2.9V, the controller needs to go nearly full duty cycle at the end. Possible with buck regulators based on P channel MOSFETs, but not necessarily every chip on the market.)
Remove lithium polymer and LiPo terms from your mind. They do not exist beyond research efforts in 1990's, despite the fact that a few manufacturers use the term for pouch form factor li-ion cells, purely for marketing reasons only. (You know, even if a technology fails to emerge, nothing prevents you from starting using the name if it sounds cool, right! Similarly, you can call a gasoline car an EV because it has electric windows. In a pouch-type li-ion cell, there is polymer in the outer package (aluminium-plastic vacuum bag), but the electrolyte is not polymer, which was the original point of the LIPO research.)