Usually the EAD gets approved after 90 days from filing. A delay in biometrics might result in a delay in obtaining the EAD. If 90 days have passed you can call USCIS and request a 'service request,' an officer will then assign you a request number and send a request to the officer working of your case to make a determination. If you want to speed up the extension of the L visa than you should file a Premium Processing Form and pay the extra fee. You can find the form on www.uscis.gov. The form number is I-907.
Estimated processing times are posted on the USCIS website. As the EAD depends on your L-2 status, it cannot be processed until your L-2 has been approved. The processing of the L filings can be expedited through Premium Processing.
EAD that can be processed are normally processed within 90 days of filing.
The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.