Did you apply for Replacement of Green Card (Form I-90) and the process is delayed?
Now you can go to your local USCIS office and request a temporary passport stamp to prove that you are lawful permanent resident. The stamp is good for one year. It is god for proof of employment authorization and travel. Schedule your INFOPASS appointment to get your I-551 stamp. Bring with you your old green card, notice of filing of I-90, and your driver’s license to prove your residence.