An L-2 spouse is employment-authorised incident to status, so working is possible in principle. Whether working for the same company is sensible is a separate question involving payroll, the ownership picture and how the principal's managerial claim is presented.
Permission and prudence are different questions
The permission side is settled by status: the spouse of an L-1 principal is authorised to work incident to L-2 status and does not depend on the principal's employer for that authorisation. The practical side deserves more thought. If a small distribution arm has three employees and one of them is the manager's spouse, the description of who performs the operating work becomes harder to present cleanly. There may also be tax and payroll consequences that have nothing to do with immigration. Dependent children in L-2 status may attend school; they do not receive the same employment authorisation as the spouse, and a child who turns twenty-one during the stay leaves dependent status and needs a route of their own.
Hypothetical example: A renewable-energy director will relocate with a spouse who has an existing remote career and a child beginning a diploma program. The first review should make a dependent-status checklist for each traveller, including passports, relationship records, and planned travel dates. A qualifying L-2 spouse has employment permission incident to valid L-2 classification, but employers may still require the ordinary evidence needed for hiring and verification. An unmarried child under twenty-one may attend school but cannot take employment on that derivative basis. The marriage certificate and birth certificate settle the relationship; the admission record settles status duration. Treat a child's twenty-first birthday as a separate planning deadline.