I get the middle point of each segment of each piece of surface, and find the closest line index (among the 4 line questions, so an integer between 0 and 3). Then I remove duplicates in the list with Create Set. If the amount of elements after that is exactly 4, this means that the piece is surrounded by all four lines.
As said above this should be changed using Curve Side. I can do that if you provide me a file with all parameters and line equations in place, so I can do it on a correct dataset.