I have been served with a lawsuit for a lease that my ex & I had gotten under both of our names. In our divorce decree, I stated him as being responsible for this debt. Am I correct to assume this since it is written in my decree of dissolution.
The creditor is not a party to your divorce. As far as the creditor is concerned, the persons whose names are on the lease are the persons responsible and whatever side-agreements the persons have among themselves do not bind the creditor.
You should review your decree. You may be able to ask the court to enforce the decree and make the former husband pay. Alternatively, you may have to pay the creditor now and enforce the decree later.
If you had liability before the divorce you have it now. You cannot adjust the rights of a third party in your divorce decree.
If you believe you have more debt than you can deal with it might be wise to seek the advice of an experienced bankruptcy attorney to determine what is the best course of action for you.