If I have older version of the green card, can I still travel while I'm in the process of renewing (I-90) my old version green card that has no expiration?

Travel with your I-797 to verify renewal

Make sure to take all relevant evidence with you when you travel. The U.S. Customs and Border Patrol (CBP) will determine if you are able to re-enter the U.S. after leaving the country, and many airlines may ask for a I-797 receipt notice to show you have already filed to renew your green card. You may also make an appointment at your local USCIS office to request an extension. CITATION: 1) https://help.cbp.gov/app/answers/detail/a_id/75/~/lpr--lost,-stolen-or-expired-green-cards-or-has-no-expiration-date; 2) http://www.uscis.gov/green-card/after-green-card-granted/renew-green-card; 2) Page 98. http://www.uscis.gov/sites/default/files/USCIS/About%20Us/Electronic%20Reading%20Room/Customer%20Service%20Reference%20Guide/Permanent-Residents4-3.pdf