Diagnosis
Your TV isn't recognizing the input signal. This is almost always because the HDMI port needs to be manually told what type of device is connected or the TV's input settings are confused.
How to Fix It
First, unplug the Fire Stick and its HDMI cable from the TV. With the TV on, press the Settings button on your remote (the gear icon). Go to All Settings > Connection > Device Connection Settings > HDMI Deep Color. Make sure it's turned OFF for the port you're using (like HDMI 1). Now, plug your Fire Stick back in. Press the Input button on your remote, select the correct HDMI port, and this time, hold down the center OK button on it. A menu will pop up—select "Edit" and rename the input to "Streaming Device." This tells the TV what to expect.
If That Didn't Work
The TV's software might be glitching. Unplug the TV from the wall outlet for a full two minutes. This performs a hard reset that clears temporary memory. Plug it back in and try the HDMI port again.
Heads Up
LG's Simplink (HDMI-CEC) can sometimes cause handshake issues. If you have problems with the TV turning other devices on/off, you can disable Simplink in the Connection settings, but try the rename fix first.