To make a long story short, I need to lock my Xbox when I'm away from the house to prevent my youngest sibling from getting into it on the occasions he's left home alone. Is there a way to lock it so that he can't use it? I searched through settings on the console but found nothing to indicate a way to lock it, such as a password required to boot. Obviously I could do something like take the power brick but I want to check for a better way.
Nope, there's no trivial way to software-lock the use of the Xbox 360 short of modding it. Taking the brick or AV cable is probably your best bet.
Set up a parental control passphrase and set the lowest ranked game that he can play to EC (Early Childhood). This worked for my brothers when I was younger and needed to go do something. Just dont make the code ABXY and you should be fine. Although, taking that brick is ultimately the end all, be all of security.