Yes, as far as immigration status goes. An L-2 spouse is employment-authorized incident to status. Whether she can teach depends separately on state teacher licensing, which immigration status does not confer.
Immigration permission and professional licensing are different gates
Hypothetical example: a Mission elementary teacher accompanies her spouse, a transferred process engineer, on L-2 status. Her authorization to work is part of that status; no separate employment authorization application is required to be authorized, and her admission record will carry the spousal annotation employers can accept. Teaching in a public school, however, is regulated by the state, and a Canadian certificate will need whatever evaluation and licensing the state education authority requires.
Private schools set their own rules. Her status ends with his, so a five-year L-1B ceiling is a household limit as well. If the couple has children, they may attend school on L-2 status but may not work.
She should begin the licensing process early, because that clock is usually the longer of the two. Hypothetical example: A packaging-process specialist moves with a spouse who plans to freelance and a child who has been offered a paid summer internship. The family review starts with the intended activity and the I-94 category for each person.
A spouse admitted as L-2S can establish work authorization from that record, but a child in L-2 may study and cannot take the internship as employment. Keep proof of the relationship and current admission documents together, because dependent status ends when the principal's authorized stay ends. If the child is close to twenty-one, build a separate immigration timeline rather than assuming the L-1B extension will preserve eligibility.