Yes. An L-2 spouse is employment-authorized incident to status under current USCIS policy, with the Form I-94 annotation serving as evidence of work authorization. L-2 children may attend school but are not employment-authorized, and they lose L-2 eligibility at 21.
L-2 spousal work authorization comes with the status itself
Unlike the TD spouse of a TN professional, Tomasz's spouse does not need to qualify in her own right to work; the L-2 classification carries employment authorization by operation of policy, and the annotated I-94 is what an employer uses to verify it. She may work for any employer or run her own business. A separate employment document may still be useful in some situations, and she should ask counsel whether to apply for one. Children in L-2 status can attend school and remain dependants until their twenty-first birthday, at which point they need their own classification, such as a student status, arranged before the birthday rather than after. If a family member is not a Canadian citizen, they need an L-2 visa from a consulate, and the appointment should be booked once the L-1A is approved. Keep every family member's status expiry aligned with Tomasz's own.
Hypothetical example: A printing-company manager expects to move with a spouse and two children. The review gives each dependant a separate identity and expiry-date check, because their ability to accompany the principal depends on maintaining the derivative classification. The spouse may have work authorization incident to qualifying L status but should carry the required evidence of that status when starting work. The children may study but do not receive that employment benefit. The family should decide in advance how an older child will maintain status after ageing out, rather than discovering the issue during a school term.