As others have said, the lancet should be changed after every use, for comfort's sake, if nothing else. Every use dulls the lancet, and the sharper the lancet the easier it goes in, and therefore the more comfortable it is.
HIV? Forget it (in this instance) HIV only survives outside the human body (or laboratory conditions) for a few hours at the absolute most. Yes, there are other blood borne diseases that could be caught from a lancet in this situation, except you'd be catching them from your mother, not your sister, because nothing hangs around on a lancet for a year.
Since it's only your mum that uses the pen normally, I'd guess that she's the one with diabetes, in which case it's a reasonable worry for you that you might eventually develop diabetes: note that I said develop, not "catch". Children of people with diabetes have a higher chance of developing it themselves.
As for your fears about HIV, I suggest you contact the Terrence Higgins Trust on 0845 1221 200. I used to work with one of the Trust's sister organisations and,believe me, we got to the point nearly twenty years when there wasn't a variation on a question we hadn't heard! They'll talk you through your fears calmly and logically and hopefully stop you worrying...
Steve