How do you calculate regulator lost current?
An XY problem?

A good alternative to the 1117 (quiescent current) for low-power applications would be the low-quiescent current LDO MCP1702, which has a 5 uA maximum quiescent current over its operating temperature and input voltage range.

Of course, a linear regulator itself wastes a lot of of power, but this should only be a concern when there is an appreciable load current during extended periods of time. In that case, a switching regulator could be a better option, at the expense of higher consumption when the toy is sleeping.

But if your toy will spend most of its time sleeping, then your overall power budget will be better off with a low quiescent linear regulator instead of a switching one.

As a final note: reducing battery voltage (from 9V to 4.5V = 3 x 1.5V AA), as Marcus Müller said, will always be less wasteful and less thermally-stressful for the regulator.