Shortened version of Lolita or lolicon which is Japanese anime/art depicting most often a young girl or preteen. The word lolicon is the synergy of 'Lolita' (see also, book by Nabakov) and the psychological word 'Complex.'
The lolli that the anime artist drew was flat-chested and big-eyed and tiny and in her panties.
A fetish that livens up bedroom activity between couples. When the lolly has been licked you then place it up your anal passage, that it out and continue licking. This can also happen between couples in that the other person licks the lolly after it has been up their partners anal passage.