If visiting LA for less than 10 days (the quarantine time) will I have any problem flying out LAX?

Most likely not, though there is talk of a federal requirement to get a Covid test before flying. It has not, however, come to pass yet. 

You should not have any problem leaving.  LA County DOES have a mandatory quarantine in place right now, but I don't know if or how they are enforcing that.

No, you can fly out. You can't do anything else out in the quarantine period.

You do not need to re-ask your question.

Los Angeles DOES NOT HAVE A QUARANTINE!!!

Direct from the State of California Public Health website:

3.    All persons arriving in or returning to California from other states or countries, should self-quarantine for 10 days [ii] after arrival.

SHOULD does not mean the same as REQUIRED

You will not have a problem flying into or out of Los Angles.

Please be mindful that Los Angeles is NO FUN right now.

It is in the low 60F, sprinkling with super strong winds.

We have not been able to eat inside a restaurant for almost a year.  We have not been able to eat outside of a restaurant for almost 2 months

There are no entertainment activities open... and outside is not exactly great as I write this.

If you need an ambulance it might or might not come help you.

If the ambulance comes and the workers determine that there might not be a good chance of survival, they may not transport you to the hospital.