LSK means "Label Skip", and you really can't get rid of the display (unless you want to reprogram the CNCs EPROMs)
Fanuc refers to the the "Label" as any man-readable information on the leader of a paper tape. Years ago, people used to punch "man readables" on the leader so you could hold the tape up to the light and read the part number, the program number, etc.. This punched pattern meant nothing to the CNC control because it was not in any recognizable EIA or ISO (ASCII) format. The man-readable leader needed to be "skipped" by the control when you tried to read the tape.
Fanuc's Label Skip function simply causes the control to IGNORE any data it reads until it sees a valid Line-Feed or EOB character. You can punch all kinds of junk on the leader of the tape, and the Fanuc will zip right by all that data until it reads a Line-Feed, then it begins reading the G-code data. Even when you're not using paper tape, the LSK function is effective, that's why any DNC system would have to send at least one Line-Feed character to the CNC before the first block of the program. Otherwise, the first block gets ignored.
LSK only goes off when your reading a program (by tape or by RS232), and the first LF has been read. Once you get to the end of the program, LSK comes back on.