Can the big "X" sign be used for purposes other than runway closure?
There are a couple of different NOTAM's stating runway closures at KLAX, including the below. Bear in mind that runways are closed regularly for maintainence (resurfacing) just like roads. No drama about that.

LAX 05/189 LAX RWY 07R/25L CLSD DLY 0800-1300 1705300800-1706011300
LAX 05/157 LAX RWY 07L/25R W 1300FT CLSD. DECLARED DIST: RWY 07L TORA 9665FT TODA 9665FT ASDA 9255FT LDA 0FT. RWY 25R TORA 10808FT TODA...
LAX 05/156 LAX RWY 07L CLSD TO LDG 1705252200-1708190659

There are also several closed taxiways.