I have a side by side LG refrigerator. Model LSC 27910TT.
The ice maker tray sets lower on left side (looking at the freezer) than it does on right side. Therefore, when water is dispensed it runs over onto the shelf below and into the ice bucket. The ice builds up on shelf and in ice bucket.
I have checked the water pressure, it is above 20 psi and the water inlet valve is working properly.

What makes the tray set unlevel? I can send pictures if this helps.