I presume that you don't mean a physical lock to secure it to the desk but a security code that needs to be entered so that it cannot be accessed remotely. If so the answer is most definitely yes and you should go for the latest WPA2 if your PC and your router support it. Without security it is possible for outsiders (possibly literally sitting outside your house) to gain access to your router and hence to your PC where with a minimum of effort they could gain access to any stored passwords, pin numbers or credit card info that you might have unwittingly stored when buying over the internet.

If you have the router manual, or the setup disk that came with it, it should be a simple matter to access the router and set up a security code.