How can I expedite an I-95 extension?

If there is premium processing attached to the L-1 extension, that is one option. If the L-1 visa is valid, that may be another, that is traveling abroad.

This is not a classification currently allowing premium processing.

To request an extension of L2 status within the U.S., you need to file Form I-539, Application to Extend/Change Nonimmigrant Status. Unfortunately, 15-day premium processing is not available for I-539 applicants seeking L2 status extensions. The only way possible to speed up the adjudication is to file an expedited request. However, you need to meet one or more of the expedite request criteria:
* Severe financial loss to a company or person, provided that the need for urgent action is not the result of the petitioner’s or applicant’s failure to timely file the benefit request or to timely respond to any requests for evidence;
* Emergencies or urgent humanitarian situations;
* Nonprofit organization (as designated by the Internal Revenue Service (IRS)) whose request is in furtherance of the cultural or social interests of the United States;
* Government interests, including cases identified by the government as urgent because they involve the public interest, public safety, national interest, or national security interests; and
* Clear USCIS error.
USCIS considers the expedite requests on a case-by-case basis, and the decision to expedite is within the sole discretion of USCIS.