A legally married spouse in L-2 status is employment-authorized incident to status and may work without a separate permission. A common-law or de facto partner is not a spouse for this purpose and receives no derivative status at all, so that person needs an independent basis to be there.
Marriage is a legal fact here, not a description of the household
Canadian households frequently treat long-term common-law partnership as equivalent to marriage, because in many domestic contexts it is. Derivative immigration status is not one of those contexts. If Priya and her partner have never married, he cannot obtain L-2 status, cannot rely on the employment authorization that comes with it, and would need his own route — his own employer, his own qualifying occupation, or a student status — arranged on its own timetable.
Couples who intend to marry should understand that the sequence matters, since the status follows the marriage rather than the intention. Where a spouse does qualify, one further point is worth planning around: employment authorization incident to status settles the immigration question but not the professional one. A spouse practising a licensed occupation still needs whatever state licence that occupation requires, and those applications run on their own schedule.