The TV screen going black momentarily indicates that the TV is adapting to changing video modes while bouncing between the Apple TV home screen, an app, a screensaver, or a program you're starting to watch. If this happens in the middle of a program or movie while you're watching it, I would be surprised (and it would indicate a more serious problem). The video mode-switching frequency can be minimized by correctly setting your TV and ATV4K devices to agree on the best available video format(s) that both support and staying there.
You don't identify a specific LG model so I don't know its full capabilities, but I'll guess it's similar to or better than my older/cheaper LG model... In your LG TV's settings, make sure that Connections > Device Connection Settings > SIMPLINK (HDMI-CEC) is turned on and I suggest turning on Auto Device Detection and Auto Power Sync (for full & proper operation of the ATV Remote). Under Advanced, enable the deep color mode for the HDMI port your ATV4K is connected to, and in general enable all the spiffy HDR10/HDR10+/Dolby Vision like capabilities that your TV supports.
Next, go to ATV4K Settings > Video and Audio > and under VIDEO select Reset Video Settings. Then, enable HDR. Then set Chroma to 4:2:2. Note that if your TV has more advanced abilities than mine, you may see additional options regarding Dolby Vision, etc. NOTE (this is important): resist the urge to turn on Match Format. Leave it off! It is the constant matching of subtle differences in content that causes your TV to constantly go black as it adapts to different frequency ranges and frame rates. I prefer to set ATV4K to match the best capabilities of my TV (and stay there). Finally, if you've got a nice iPhone, scroll down to CALIBRATION and do the Color Balance process.
Hope this helps.