An L-2's status is not tied to a particular employer, and an L-2 is generally permitted to remain in the U.S. while the L-1 travels. Assuming there are no other unknown facts not presented here, you should be OK to start on the H-1B October 1st.
Khurgel Immigration Law Firm
Kindly note that this posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Remember, this site is akin to an internet blog. Do not rely on information here to make important decisions in your life. Make an appointment to meet with a licensed attorney in his or her office (or via Skype or phone) to obtain competent personal and professional guidance -- Khurgel Immigration Law Firm -- Representing Clients in all 50 States and Worldwide / 4199 Campus Drive, Suite 550 / Irvine, CA 92612 / Office: (949) 509-6515 / Direct: (949) 535-6331 / Web: www.khurgel.com / Email: firstname.lastname@example.org / Attorney Khurgel is a former USCIS and Department of State Embassy Officer.
Your situation is clearly ripe for a full fledged consultation with an experienced immigration attorney not a quick post on AVVO.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
I don't want to scare you. But, there is a good chance that your L-2 is no longer valid ... quite a bit depends on how the L-1's employer did (or didn't) do payroll, etc.
You had better talk to your employer's immigration lawyer IMMEDIATELY.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- firstname.lastname@example.org -- www.capriotti.com -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Need to discuss in detail with an immigration lawyer
John Lassen 1-877-252-4630