"ARP Spoofing" is the technique you need.
The Wikipedia article explains the basics and lists some tools:http://en.wikipedia.org/wiki/ARP_spoofing
The short explanation is that each computer on the LAN has a MAC address and an IP address. Each Ethernet frame has to be addressed to the target computer's MAC address. As you've discovered, you can't just change the IP on your computer since the OS will check to see if anyone else is using the IP and refuse if it is in use. Instead of completely taking over the IP address (in which case you need to crash/flood/disconnect the client), you can just convince the server that your computer's MAC address is associated with 192.168.1.200. Using ARP Spoofing software, you can pretend to own the client's IP address knowing full well that it is in use.
ARP spoofing is a targeted attack so you can convince the server that you own the client IP address without affecting other computers. For example, the client could still browse the web and the return traffic would reach him and not you.
Good luck with your lab.