Does Arduino use step down voltage regulators?
Arduino Leonardo, like the Uno, uses an NCP1117 linear regulator (LDO), which can supply 800 mA, but at 11.1 V input that would be 4.88 W, so thermal protection will set in much earlier.  

Using USB is a possible solution, but keep in mind that USB doesn't have to supply more than 100 mA, you'll have to negotiate for 500 mA. And Arduino is not designed for low-power, I don't know what the Leonardo consumes, but I guesstimate the Uno's supply current at 50 mA, so powered from USB that may leave too little for for instance a series of LEDs.

Your own switching power supply looks like the best solution. Bypass the NCP1117 and supply it directly with 5 V. A 12 V to 5 V buck converter should be able to have a near 90 % efficiency. If the dingus would need 50 mA it can run for more than 48 hours on the LiPo battery.  

Further information
Arduino Leonardo schematic