My daughter aged 12 uses the term 'on my larry' or sometimes 'laz' to indicate on her own. My elder daughter aged 19 used to say it. My friends daughter who lives in Letchworth uses it. We live in Hertfordshire so I don't know if its local, but we can't find any reference to larry and being on your own, in any slang, or playground talk. I really want to know who the larry is! We would love to know ! any suggestions?
I think it comes from "on my Larry Jones" - i.e. rhyming slang, although the more common phrase is "on my Jack (Jones)" - -I have no idea who Larry Jones might have been though