No. L-2 status is limited to a legal spouse and unmarried children under twenty-one. A common-law partner is not a derivative under the L classification, so she would need her own basis to enter and remain in the United States.
L-2 follows the marriage record
Derivative L-2 status is available to the spouse and unmarried children under twenty-one of the L-1 employee. A common-law relationship recognized in Saskatchewan does not create a spouse for this purpose; the relationship must be a legally valid marriage. A partner who is a Canadian citizen may be able to visit, and if she has her own professional qualification she might consider TN or another classification with her own employer, but she cannot rely on the specialist's status. Couples in this position sometimes marry before the transfer, which then requires the marriage certificate to be included in the family's documents. Children of the specialist from the relationship, if under twenty-one and unmarried, can qualify as L-2 dependants on the strength of their birth certificates regardless of the parents' marital status. Plan the partner's route separately and early.
Hypothetical example: a biodegradable-packaging company transfers a specialized process analyst with a spouse and two school-age children. Begin with civil documents and the principal's petition record, then map each dependant's passport validity and intended admission dates. A spouse in L-2 status generally has work permission from the status itself; the admission record is important evidence for an employer. The children may attend school but cannot work, and their eligibility ends at twenty-one. The decision for the household is whether the analyst's five-year L-1B ceiling leaves enough time for the children's school plan or calls for a different strategy.