1.How to keep the card
a. Stop lying to government officials
b. Get a re-entry permit
c. File an N-470, if appropriate.
Additional comment ... hire an attorney.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Get a re-entry permit. That will allow you to stay out the US for more than 6 months. File an N-470 to preserve eligibility for naturalization. If you do things right, you should be fine considering you're working for the US government.
You did not say what company you were working for in Iraq. If you are working for the U.S. government, you may be eligible to file a case to preserve that time for residency purposes. If not, you've got some tough decisions to make about whether you want to keep your green card. Consult an attorney. Good luck!
Also see the link below on re-entry permits.