If you do connect to the wired LAN and the Internet at the same time on the same machine, then your lab LAN will be connected to the Internet, and will be vulnerable to attack through your machine. If there is a reason for keeping the lab LAN separate from the outside world, then don't use your machine to connect to both at the same time. Use a separate machine for each environment.
If you are go ahead and connect to both, XP can do what you ask. All you need to do is connect to the wireless network, then set a route for the lab LAN out the Ethernet device. The default route will point to the wireless device, giving you access to the Internet, and packets to addresses on the lab LAN will go out the Ethernet device. Also, if the lab network is small, you can add the names and addresses of the lab machines to your hosts file so that your machine will be able to address lab LAN machines by name. Get the lab network numbers from the people running the LAN, or just ask them for a route command that configures your machine. If you need help with route, tell us what you need.