Can you clarify exactly how it's connected? If I'm reading it correctly, your LG is connected with micro-USB, which runs to HDMI wMHL support on the other end (into the TV)?
Provided your phone can output to HDMI over mUSB, this setup should just "work". The TV has no way of distinguishing between a phone/cable box/DVD player etc.
Video "out" via microUSB isnt widespread though AFAIK. MHL was designed by Nokia, Samsung, Silicon Image, Sony and Toshiba, and adopted by them. Others can implement, but not 100% convinced all (most?) do. Typically, competitors microUSB port is limited to "input" to the device; of either power, or sometimes external storage.
I don't believe the issue is with the TV though, more likely in the phone's abilities.