Here's official information on what to do if you lose your Green Card, and how to replace it.
Quote Quoting Lost Green Card
If you are outside the U.S. and have lost your alien registration card, contact the nearest American Consulate, USCIS Office or Port of Entry before attempting to file a Form I-90. If your Form I-90 application is approved, you will be mailed a replacement Permanent Resident Card,Form I-551, with a ten-year expiration date from the date of issuance.