Yes. L-2 spouses are employment-authorized incident to status, and the admission record annotated for an L-2 spouse serves as evidence for employers. Children may study but not work, and dependant status ends at 21 or on marriage.
Dependants of L-1B and L-1A hold identical L-2 rights
There is no distinction in dependant treatment between the two L-1 subcategories. A spouse accompanying a Sainte-Brigitte-de-Laval L-1B specialist may take employment with any employer, run a business or work as a contractor on the strength of L-2 status, without first obtaining an employment authorization document. Any professional licence the spouse's occupation requires in the U.S.
state is a separate matter. Children may enrol at any level of school but may not work, and their status ends at 21 or on marriage, at which point a student classification or another route in their own right is needed. Two timing points matter for L-1B families specifically.
The principal's stay is capped at five years rather than seven, so a household planning around the maximum should use the shorter figure. And each dependant's admission is tied to the principal's petition validity; when the principal extends, dependants must extend too, and a dependant whose I-94 expires earlier than the principal's loses status regardless of the transferee's position.