Can't find low battery threshold setting (Samsung Galaxy S3)
There is no setting available in any Android ROM that has the battery threshold setting. 

From the previous answer given, it is built in.

Only course of option is to roll your own Android build, with the hard-coded value adjusted, but, and is a big but indeed, it is not the recommended route to take, as the code behind Android to handle the battery mechanism varies from chip-set to chip-set and to each and their own manufacturer. 

By adjusting it, there could be invariable damage to the battery as a result, since the threshold is specified, by "tweaking" it could affect the battery in the long run and possibly end up shortening the battery life also.