Yes. An L-2 spouse is employment-authorized incident to status and may be self-employed or employed once admitted with an I-94 reflecting L-2 spouse status. Business licensing and tax registration in the state are separate steps.
The immigration permission is broad; the state paperwork is hers to do
Hypothetical example: the transferee's wife runs a bookkeeping practice for small farms and wants to continue it with U.S. clients. L-2 spouse employment authorization incident to status covers self-employment as well as wage work, so she may operate a business once admitted; the annotated I-94 is her evidence. What the immigration status does not do is register her business, obtain any state licence a bookkeeping or tax-preparation practice needs, or resolve her cross-border tax residence, which an accountant should address before she signs clients. Her admission period follows her husband's L-1A validity, so client agreements should not assume more time than his status provides. Their children may attend school as L-2 dependants but may not work, and each ages out at 21. If she also plans to work for the U.S. company, that is permitted, but the company's payroll and the petition's organization chart should reflect it accurately.
Hypothetical example: a transferee's husband, a choral conductor, accepts occasional paid engagements after the family relocates. After admission in L-2 classification, an unexpired I-94 carrying the appropriate notation is the practical record to show a prospective engager; a concert contract does not replace it. Before accepting work, he should confirm the contract's tax and local registration effects. The principal still needs one qualifying year abroad in the three years before the L-1 filing or admission, and L-1A time has a seven-year limit, so the family's commitments should be revisited before renewal.