I've seen various fixes and have tried several (all with varying degrees of success - explained below), and this is the sort of pertinacity thing which really annoys me: no icons in LibreOffice for the Zotero toolbar, although the toolbar works fine.
Upon first install of the LibreOffice (LO) plugin, there was a 'flicker' of icons: they came and went very quickly in LO within a second or so. I searched for the solution in Google and found an article suggesting manually setting your LO to point at Java (which I'd disabled, following this tip). I have since enabled Java but I still cannot see any icons. Read through a long couple of questions on the Ubuntu Forums, another few at the Zotero forums...finally found one suggesting setting the icon size in LO to 'large'. I did this and played with the themes in LO (there are only two installed, humanity and galaxy, so it didn't take long!). Whatever I did seemed to 'update' the unity icons as the icons reappeared for both themes. I even set the icon scale back to automatic.
All was fine for a couple of minutes, but then I got to installing dictionaries for my locale (en-GB, for some reason, LO doesn't pick it up automatically and gives me AE) and then I flipped back to LO and the icons had disappeared again. Playing with the icon settings did nothing either.
There probably is an answer somewhere, but I've been trying to fix this by trawling through forum pages from years ago for about 30+ minutes now and I've had enough. Direct responses and/or a check list would be great, telling me how to manually point the plugin at the folder where the icons are stored (they must be somewhere, right?!) would be ideal.