It depends

If the person leaving was on good term with you, has been a good employee, and well liked by others, then yes, take the person to a lunch, give a small gift, or even better - organize your whole unit together and allow everyone to pitch in for the farewell.  

If this persson is leaving contentiously or because of conficts with you/your organization, you have a few choices: You may simply join others for the best-wishes (if anyone initiates it), or you don't do or say anything. This second approach may sound rude, but you need to send a message.