Yet, at the LAX check-in counters, the lines are designated so that only EXPs may use the F lines, while both GLD and PLT are listed on the J lines (which are often much longer).
The line you refer to at LAX is -not- a First Class checkin line. It's an EXP checkin line.
You'll find both biz-class and FC checkin lines at some airports (such as LHR). In that case, PLTs may use the FC checkin lines.