TBIT is between T3 and T4. T3 doesn't have elite lines for 2 reasons: most of the airlines flying out of T3 don't have elites (exception is AS), and there are so few flights out of T3 these days that the TSA outnumbers the pax at the times of day that I've been at T3. There simply aren't the kind of lines that T4 gets. I thnk there isn't an elite line at T1 or T2 either (never seen it, and those terminals do get huge lines, and in the case of T2 there is significant international premium traffic).
I guess the real problem at LAX is that the TSA is down 700 headcount from their peak staffing at LAX, and that is a lot of security screeners to be missing -- making long lines at peak times unavoidable. Plus the nature of eastbound traffic from LAX concentrates a lot of flights into a few hour window (morning and night). Making it unlikely that LAX will ever be staffed to make for short security lines, unlike some other airports.