Is there maybe someone here in lyx community who has the knowledge and is interested to make that work (and probably many scientists happy)?
If it can put a format like \cite{...} to clipboard, I have a patch to make lyx paste such kind of strings as a citation. It's not identical as the push, but I prefers this way more. If you need I can give you my patch. But you have to patch the source code and compile your own version. You can also find the patch at lyx-devel list. Hangzai