What do you mean "LCD"? Liquid crystal displays do not have Ethernet. Perhaps you a referring to a television. Modern televisions use Ethernet to set the clock to the correct time, download firmware updates, and to run all those video apps that commonly come installed on the TV (oh, and to track your behavior for marketing data).
When you plug your TV into your router using a cable and connect your computer via wi-fi you are connecting them to the same network (your home network), part of which is wired and part of which is wireless.
So, if "I" refers to your computer, you would already be connected to wi-fi. If "I" refers to the TV, then no, you won't be able to connect to wi-fi because the TV is already connected by Ethernet cable (or it doesn't have wi-fi connectability). If it does have wi-fi connectability, the TV typically allows it to connect to your network only one way or the other. You can usually configure which one to use in your TV's settings, although I have heard of a TV that uses the Ethernet cable if it is plugged in, and uses wi-fi if the Ethernet cable is not plugged in.