The last 10-9A I have from LAX is from 2008, so there might be a few differences.
Looking at the section under 6L, 7L/R, 24L/R, and 25L/R, you see three distinct headings:
1) Required RVR for takeoff, depending on operating lighting (500 or 1000 RVR)
2) Adequate visual reference RVR/visibility
3) Standard takeoff mins
The first heading describes the minimum RVR allowable for takeoff on those runways. The far left column shows that if you have centerline and high-intensity runway lights (CL & HIRL, respectively), operators are allowed to depart as low as 500 RVR. However, it further describes what's often written into an airline's ops specs: At least two RVR reports are required in order to utilize those minimums, and all are controlling. Going back to the example in my last post, you would need the TDZ, mid, and rollout RVRs to all show 500 RVR or better. However, because only two are required, it is still legal to depart when the RVR report is 500/500/missing. Important: Not all aircraft may utilize these reduced takeoff minimums. They must be approved through ops spec C078.
The column to the right is much the same as the first column, except that it restricts carriers to 1000 RVR if some of the runway lighting is inop. 1000 RVR is allowed if only the centerline lights are operational, or only centerline markings/HIRL are available. Again, you would need to have 1000/1000/1000, or at the very least, 1000/1000/missing (1000/missing/1000 is also legal).
"Adequate Vis Ref" describes takeoffs at or above 1600 RVR, and requires one or more of the following markings/lighting systems to be operational: HIRL, CL, or RCLM (runway centerline markings). If one of those aren't available, you can often still depart if the visibility is reported as 1/4sm, as long as you can identify the runway surface and maintain directional control. This is also described in C078.
"STD" mins (far right column) simply describe the standard takeoff minimums listed in Part 91. This would be used by operators that don't have ops spec C078, so it typically doesn't apply to your standard 121 carrier.
The "Other" section under the "Rwy 6R" heading shows the required ceiling and visibility for departure if you cannot maintain the required climb gradient shown for that runway (281'/nm to 400'). Because the other runways have standard climb gradient requirements, a separate section for "Other" isn't necessary.
Clear as mud? Ops spec C078 will describe all of the requirements for departing with less than standard takeoff minima (2400 RVR for 3&4 engine aircraft, and 5000 RVR for 1&2 engine aircraft).