Can I apply for EAD extension based on L1/L2 extension receipt?

While your spouse is able to work for 240 days following the receipt of the L1 extension request, that same privilege is not allowed at present for persons working on EAD’s. You would have to leave the job when your  EAD expires until the time that your new EAD is approved. On the question of whether you can apply for an EAD extension based upon the receipt, that is questionable. A better solution would probably have been for you to have submitted the EAD along with the I-539 when you requested the extension. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

You may apply for the EAD now. You should have applied for it with your I-539/L2 extension. The EAD will process in 90 days depsite his extension. Best of Luck!