A spouse admitted in L-2 status is employment-authorized incident to that status, which covers working. Owning or operating a business raises separate licensing, tax and corporate questions that immigration status does not answer.
Authorized to work is not the same as ready to trade
Hypothetical example: the specialist's spouse runs a small catering business in Coaldale and wants to restart it in the United States. Employment authorization that comes with L-2 status addresses the immigration side of working. It does not obtain a food-service licence, a business registration, a state tax account or insurance, and it does not decide whether the enterprise is worth starting.
Take those questions to the appropriate state and municipal authorities and to an accountant. Children admitted as derivatives may attend school but may not work on that basis, and derivative eligibility ends at twenty-one, which matters if the assignment runs toward the five-year maximum for L-1B status. Confirm every family member's citizenship separately; Canadian permanent residence held by a spouse is not Canadian citizenship and can change the procedural steps that person faces.