I-765 is an Application for Employment Authorization (http://www.uslegalvisa.com/en/immigration_forms.html). I-766 is an actual Employment Authorization Card.
L-1 visa holders can file for a green card and you might be eligible for the permanent resident status as a derivative. However, as a spouse of L-1 visa holder, you may file for the employment authorization independently. Please contact an experienced immigration attorney to discuss specifics of your case and your eligibility for an adjustment of status (AOS). Immigration law is a federal law and you can hire a licensed attorney from anywhere in the country.
The responses and information are intended to be general and should not be relied upon for any specific situation. Best of Luck!
Alex Meyerovich, Esq.
The I-766 is a secure EAD that she shouold receive after filing the I-765 EAD application. Information on the I-766 can be found here http://www.uscis.gov/propub/ProPubVAP.jsp?dockey=5c04c0eba68f7b06adfddc71b4fd9ce7.
If you are in the USA on an L-1A, you may wish to file an I-140 Immigrant Petition for you through your employer and an I-485 Application for Adjustment of Status to Permanent Residency for you and your wife. When she files the I-485, she can also file the I-765. If she and you are not ready to file the I-140 and I-485s, she can file an I-765 based on the L-2 status. The I-766 based on the L-2 should be valid until the expiration of the L-1. The I-766 based on the I-485 would only be valid for 1 year.