I'm not even remotely sure how feasible this is, even with a 6 hour layover.

Suppose you land "on time" at 1 PM, and have a connecting flight at 7 PM (guessing your flight will board at 6:30).

Here's the logistics:

By the time you deboard, check your bag (somewhere) at LAX, and get outside, its probably 1:30

Stand in line, grab a taxi, tell the driver to take you to the Santa Monica Pier.

Its probably $40 one way

By the time you arrive at the pier, its likely pushing 2:30.

Take a walk, spend 2 hours max. at the SM Pier and/or 3rd Street Promenade

at 4:30, get another cab to LAX. It will take at least an hour, given rush hour possibilities.

Arrive 5:30

By the time you complete security checks (are you Elite?), its possible it takes 45 minutes for screening.

Just make it for boarding.

So you get about 2 hours max.

If your arriving flight is delayed and/or there are traffic issues, all those have to factor in.

You might be better allocating only an hour at the beach to be safe.

Its a lot of work for a one or 2 hour walk

Might be better if your layover was longer.

I wouldn't do it, too risky.