I'm looking to travel next week but don't have a photo ID and need?

and i'm leaving from LAX and they said if you are over 18 you need a "government-issued photo I.D." now I lost my California ID card...and I know it takes weeks to get one, is there any other alternative?

Many airports will accept a reasonable photo ID (bank card with photo, school ID, employee ID, etc.). You may be subject to more scrutiny at security, however.

I don't think you will find an official and definate yes answer from the TSA or the Airlines, because they don't want to tell everyone they can fly without ID. But I have seen other people do it before. They will probably put an SSSS or some other kind of code on your boarding pass when you check-in, so that when you go through the security line, you will be given the extra super dooper security check by the pointy object patrol. So allow yourself some extra time to get through security. And bring any ID that you have, even if it's not govt. issued. That will probably help. For more info check out this story from NPR about flying without ID http://www.npr.org/templates/story/story.php?storyId=6657697

Here is someone who says it is not possible.
http://ioerror.livejournal.com/388052.html?nc=11

And another who said they did
http://www.cs.berkeley.edu/~daw/faa/noid.html

There is also a landmark case about it (though I have read in some places that it has been overturned or that it is limited in jurisdiction)
http://www.wired.com/science/discoveries/news/2006/06/71115

I think you should try getting a driver's license (some states issue them the same day), or some other photo ID, but be prepared to take extra time through security. Make sure you have a backup plan in case you are not able to clear