According to a recent USCIS policy, your green card renewal process should not be affected by your criminal record (after all, you are a permanent resident of this country and you're just applying to renew your card, not your status). That being said, if the crime you were charged with (and it sounds like you were, in fact, charged with shoplifting, although not formally convicted) makes you removable (deportable), you can be put in removal proceedings. Whether or not you're removable - I would not be able to tell you unless I look at your court documents and learn more about your case. In your situation, I would definitely consult a lawyer - it sounds very serious to me.
What is meant is that an attorney needs to look at the actual criminal conviction order and the criminal law that you violated. We cannot tell which state you were convicted in. This can make a difference, as well. Some shoplifting convictions are punishable as a theft.
The attorney should determine the maximum possible sentence that can be imposed for a first offense of the type committed. Even if you did not plead guilty, but merely did Community Services, you may still have a conviction for immigration purposes. The issue is whether the conviction is still a deportable offense. Also, if so, whether you can file for and get relief from removal.
In general, theft is a crime involving moral turpitude, but some of these crimes may create different issues depending upon the law. If you eventually have two convictions, then you likely will have a more serious problem. One minor drug offense for minimal cocaine possession or selling flour for cocaine can result in a deportation hearing before an Immigration Court.
In addition, you may want to know whether or when you should file for citizenship by naturalization. Perhaps, you are actually a U.S. Citizen because one of your parents became Citizens before your eighteenth birthday. However, this law has changed and some need both parents to be naturalized. You should review these issues and take responsible action. This way, you will hopefully naturalize and have a U.S. Passport in your hands before your next trip outside the U.S.
This, among other often unknown challenges is why we recommend an appointment or teleconference with an experienced immigration attorney. You should learn what can happen, has happened, and what you need to do as a result to avoid challenges in the future.
The above is general information and does not create an attorney client relationship.
You need to bring your criminal records for a consultation to get a full analysis from an immigration attorney. It sounds like you were formally charged. Question is whether you have a conviction for immigration purposes. If you obtained a pre-trial diversion and your charge was dismissed, then you may not have a conviction. If your disposition was a withhold adjudication, then you have a conviction. If you do have a conviction, shoplifting would likely be considered a crime involving moral turpitude. However, if you do have a conviction, it sounds like your case may fortunately fall under an exception, the petty offense exception. Consult a competent immigration attorney so that you can get complete analysis. Good luck!