1/2 hour isn't much time for these to get frosty, I'd expect it to run nearly continuously trying to cool if there was a leak. Unless it was very empty and the comp was overheating, the circulating R-134a provides cooling to the compressor. I can't read your temp on the infrared meter, what's it say? Also when it stops is there a bad noise?

There's a test button on the main board, probably an arrow pointing toward it or nearby. Push it once, it should beep and enter forced run mode. It only stays in forced run a few minutes but it'll bring comp up to full speed/voltage at least. Listen for buzzing or abnormal noises from compressor. I believe this is a variable speed compressor, makes them hard to diagnose as amp draw and voltage is also variable.

Check your owners manual for longer term sealed system warranty, you might have 7 to 10 years on it if your lucky. At that point call a tech.

Any errors on the display? ER xx would be the format.

If compressor dome is 131f that's pretty hot. Is the high side output line and condenser warm/hot too?

You've tapped the sealed system? Hopefully on process or suction tube? What's the reading? R-134a pressures and Temps run pretty close. So If the evap is 50deg the pressure is close to that. Low side pressures should be right around 0 with comp running and evap frosty.

==>Is there a led flashing on the board?

You have a variable speed linear compressor so you can throw out most of what you read online about compressor diagnosis unless it is specifically about linear compressors. They are difficult to troubleshoot as you can never know what the board is trying to do with that compressor. In theory the forced run mode that it enters when you press the button on the pcb should ramp up the voltage and the compressor to its max speed however that mode isn't active long enough to see much in the way of frost patterns.

Check you owners manual you may have 7yr sealed system warranty.

Those LG linear compressors​ tend to have problems with their internal valves that hinder or stop their ability to compress. Often making a loud buzzing once valve breaks. I've changed more than a few.
If you are lucky and LG pays for the part the labor may still be $300 or more if it isn't covered, your owners manual will have info.

You are welcome. Its sad but 7-10 years is becoming the new norm in appliances. I personally own a 20 yr old SxS, and a 10 yr old basic for the garage. The SxS looks old but it has 0 computers, it stays cold and I'd trust it over a new one. Bought for $125 off Craigslist 8 yrs ago. It looks old but it works.

My standard advice on replacing is spend as little as you can for the features you need. That way you'll be less upset when it dies young. Avoid the gimmicky ones with TVs, coffee makers, soda makers, etc... Avoid Samsung (401 model #s if Kenmore). Avoid Daewoo (111 model #s if Kenmore). Their prices may look good but you'll pay more on early repairs.

Good Luck

Ambient temps would need to be very high for a failed cond fan to cause issues. Its just the laws of physics. As long as that compressor can produce a hot / high pressure gas and there is any heat exchange to allow that gas to become liquid at the condenser it will cool when it expands in the evaporator.

Having changed many of these compressors I'd say it's either the compressor itself or a restriction in the system that is causing the compressor to trip off on safety. I'd need to tap and get low side pressure to narrow it down. Given the buzzing compressor however and the fact that we change these nearly daily I'd go with that diagnosis.