For TSA lines, I use pre-check in Terminal 6. The pre-check line is usually about 6 people deep and I may clear through TSA in about 12 minutes often less.
If you don't have pre-check, I can't tell you how long it takes to go through the other lines including any priority line.

You may pass through TSA in other terminals that are connected. reference: https://www.flylax.com/inter-terminal-connections

In and out of LAX, I am running about 90% on time. (The last flight outbound LAX was delayed about 40 minutes for the flight crew to arrive, then we had a small 10 min delay at SFO when the tik-tok-ers had to be first escorted off the plane by police)