I presume that when you filed your application to become a Lawful Permanent Resident all of the information you supplied to the USCIS was true and correct to the best of your information, knowledge and ability. If and when you may apply for naturalization, you will need to respond to questions about having filed tax returns, having identified yourself as a resident of the U.S. in those tax returns and about not owing past-due taxes to the government. If at the time you file a naturalization application you have not paid all of your tax obligations, it would be wise to include a notation in your application that states you have a payment plan approved by the IRS and you are complying with it, and be prepared at your interview/examination to provide copies of the IRS payment plan and evidence that you are complying.
In connection with reaching a payment plan arrangement with the IRS, I recommend engaging a local tax attorney to help you.
David N. Soloway
Frazier, Soloway & Poorak, PC
1800 Century Place, Suite 100
Atlanta, Georgia 30345