Yes. You can file for a change of status through USCIS. Make sure that you have a valid EAD that will remain in effect until your status is changed to L2. After your change of status to L2 occurs, you must then apply for a new EAD (and pay the fee) to work with an L2 status.
You can apply to change your status if you lawfully entered the U.S. on a visa of some kind, your non-immigrant status is still valid, you’re in total compliance with the conditions associated with your visa, and you’ve not committed a crime.
Do not presume that your status has changed until you’ve been notified that your change of status was approved by the USCIS. Until you get that approval, do not change your current activities. If you change your current activities before you get your official approval, you could lose your non-immigrant status and be deported and prevented from returning.
Going through the process can be confusing for many people. If you’d like to talk with an immigration attorney to get some advice, consider. We are a marketplace of attorneys who provide legal advice at an affordable flat rate.