The LAPD is currently conducting a backround investigation on me. If the investigation goes good I will have a psychological interveiw, and then polygraph. Any advice that might help would be greatly appreciated.

Be honest about your past and don't lie.  If they tell you that you are lying or some other BS like that then stick to your guns and don't go and change your answers.  They might try and intimidate you basically treating you like a criminal trying to break you down.  Don't worry about the psychological...it's a joke.  

Adam...I'm gonna take a different approach here. I'd take it all seriously. I've worked recruitment and know how serious the officers tasked to investigate new hires take it. Teh psych eval is tedious to say the least, but the Agencies doctor is trained to spot bullshit artists. The test, in the early 80's when I started, was around 800 questions. Some of the questions are repetitive...like; Do you love your mother.....do you love your mother more than your father....If they ask you on the test if you'd like to be a librarian..if you would, answer yes, if not answer no. The reason I'm telling you this is:

1) Some try to come off as being goody two shoes

2) Some try to come off as someone they're not

Trying to bullshit the test is about as hopeless as trying to bullshit the shrink.

Polygraphs are weighed heavily in the application process...a pretty high percentage of applicants fail it because of dishonesty. Just be honest...like I said...trying to bs your way into a sworn position is hopeless....sure it's been done...but liablity insurance is costing cities and municipalities an arm and a leg these days...especially for LEO's and they're taking less and less chances. LAPD is a top notch agency...they get the best people and they know what they're doing...trust me on that[;)]

Good Luck!