Do I need to take only avis shuttle bus from la airport to your avis parking lot? I have a friend also willing to drop me off to avis parking lot to save some time instead of waiting for avis shuttle bus at airport.

We took the bus. Didn't have a very long wait.

The shuttle and cars share the same roads so both will be the same journey time. They'd likely need to park outside Avis compound so might be a short hike to office too

Wait for the shuttle - private cars will drop yiu off a good 350 yards away

Just wait for the shuttle. It comes pretty quick, plus the traffic congestion in LAX is horrific. Stick with the shuttle.

It doesn't take too long for the Avis shuttle bus at LAX to arrive. I do not think that they allow personal vehicles on the Avis lot so it may be more trouble to have your friend drop you off there.