In answer to your question - if there was blood on that lancet and the child or anyone pricked themselves and that blood entered into the bloodstream, yes there is a chance with that small puncture. It only takes a very small amount of blood.
If you'd asked me that question - do you have any diseases I should be worried about? - five years ago, my honest answer would have been no, I don't have any diseases and I would have been honestly wrong, not knowing I had Hep C until 2006. Particularly with a child, I'd have the testing done simply to be on the safe side as the person themselves might not know their own status.
Good luck.
I think it would be prudent to ask the person who's test kit it was (and how did this child get access to it one would think things like this would be off limits) if they have any disease in the first place. Most likely they dont and therefore it's a moot point.
Anyone who has had a needle stick from a previously used needle should be tested for blood borne diseases. HCV in particular, will not show up for about two to three weeks from exposure and only at that time by having a HCV/RNA by PCR test done.
Good luck..
Will
Only if the lancet was previously used by someone with blood borne disease.