Yes. An L-2 spouse is employment-authorized incident to status and may work for a U.S. employer, a Canadian employer or himself while living in the United States. Tax and payroll treatment of cross-border remote work is a separate matter for both employers to resolve.
Incident-to-status authorization covers any lawful employer
Under current USCIS policy, the spouse of an L-1 transferee is authorized to work by virtue of L-2 status, evidenced by an admission record carrying the spousal notation, without applying for a separate employment authorization document. The authorization is not limited to U.S. employers or to particular kinds of work; continuing to perform his Canadian job from a U.S.
residence is lawful employment from the immigration standpoint. What the immigration rule does not address is how his Canadian employer handles payroll withholding for an employee now resident in another country, or how his own tax residence changes, and both employers should take advice on that before he starts. Children in L-2 status may attend school and may not work in any capacity, and a child who reaches 21 during the assignment must change to another status before that birthday to remain.
Because his authorization depends on her L-1B, the household should note the five-year L-1B ceiling and plan any longer stay around a different category for one or both of them.