No. L-2 status is available to the legal spouse and to unmarried children under 21. An unmarried partner does not qualify, and would need her own basis for entry such as a visitor admission or an independent work or study category.
Marriage decides derivative status
Derivative categories in US immigration law follow the legal definition of spouse, so a common-law relationship recognised in British Columbia does not translate into L-2 eligibility. Hypothetical example: the Lake Country planner has lived with his partner for eight years; unless they marry before the visa application, she cannot accompany him as a dependant. If they marry, she becomes eligible for L-2 and, as an L-2 spouse, is employment-authorised incident to status, which is a substantial benefit compared with visiting.
Children of the relationship who are his children qualify as L-2 dependants if they are under 21 and unmarried, regardless of the parents' status. If the couple prefer not to marry, her options are to visit for limited periods, to study on a student visa, or to find her own employer-sponsored category; none of these give her the right to live and work in the United States for the length of his assignment. This should be decided before, not after, the petition.