Is there any power shell command in exchange to do an e-discovery only on particular item (Lync item) and move the result to another mailbox under new folder?

You are welcome to read the documentation and experiment to learn if all the requirements you list can be satisfied by the standard function set.

https://technet.microsoft.com/en-us/library/dd298064(v=exchg.150).aspx

Nothing I know if in Powershell can do all that you want however you might be able to do so with EWS https://msdn.microsoft.com/en-us/library/office/dn535505%28v=exchg.150%29.aspx?f=255&MSPPError=-2147217396