Hello, My green card expired about 7 years ago. I'm about to file a renewal form and I'm aware that this process can be few months long. I just find out that my mom has been diagnosed with a lung cancer. This is a very urgent matter and I will must leave US for some time to be with her ( she lives in Europe) If there is anyway to speed it up a renewal process for emergency situations like this one ? I should be able to provide a medical evaluation of her condition if necessary. What I have to do? Thank you in advance.

So you've been living in the U.S. this whole time, right? Although the card expires, permanent resident status does not expire. You've been maintaining residence in the U.S. so you're still a legal permanent resident. That's fine. How long the card has been expired is not relevant. What is relevant is that you need to renew it now.

Once you file the I-90 to renew your card (which you must do while in the U.S.), you can go in for an InfoPass appointment at a USCIS office and get an I-551 stamp in your passport. Green card is I-551, and this temporary stamp is equivalent to the card in every way, allowing you to travel and work during this time. If you plan to leave for about a year or more, you should apply for a Re-entry Permit before you leave.

Is your status permanent or conditional?

kcomissiong has a good point. If it was 2-year conditional permanent residency, and you didn't file for Removal of Conditions, then your permanent residency would have been lost a long time ago.