I would definately not recomend buying medical equipment or supplies from Ebay. Lignocaine (and Xylocaine & all other generic brands) are intended for use & purchase by the professional, i.e Dr, nurse, dentist or trained piercer, not a random ebay bidder!
(No offence intended Loubylou X)
Although a solution such as this would have a numbing effect, its a bit un-necessary.
The 'clack' sound made by the piercing gun is more scary than the actual sensation.
The pain is really only a sting, the only soreness comes later (if you get any), when washing hair, laying down on your side, that sort of thing, and the anaesthetic will have long worn off by then.
if your daughter is old enough to have her ears pierced, then she's old enough to feel it! lol x
p.s: i am a pro body piercer, check out my profile x
just to add, if your daughter is planning to have a cannulae (needle) piercing on her ear, then i can see the point of a local anaesthetic, but i personally would go for an actual 'freeze' spray (i wont give the name, so's not to tempt anyone, lol !) which literally freezes the area for up tp a minute or so.; incredibly effective for ears & navels xx