Yes. An L-2 spouse is employment-authorized incident to status and may be self-employed, provided the admission record carries the spouse annotation. Children in L-2 may not work.
Self-employment is employment, and the spouse is authorized
The spouse of an L-1 principal is treated as employment-authorized incident to L-2 status after admission, and that authorization is not limited to a particular employer, so a home bookkeeping practice serving Canadian or U.S. clients is permitted. Confirm on arrival that the I-94 shows the L-2 spouse annotation; if it does not, request a correction before starting work, because employers and banks rely on it.
Register the business and pay taxes as any U.S. resident would. Children in L-2 status may attend school but hold no work authorization, and a child who turns 21 during the assignment must find an independent basis to remain.
If the spouse plans to accept a salaried position instead, the same authorization covers it. None of this depends on the principal's plant or on the length of the assignment; it depends on each person's own valid L-2 admission and passport validity.