L-2 status is available only to a legal spouse and to unmarried children under 21. An unmarried partner cannot hold L-2 and would need their own basis to enter and remain, such as visitor admission for short stays or an independent work or study status.
Only a spouse holds L-2
Hypothetical example: the engineer has lived with her partner for nine years without marrying, and they have a six-year-old child. The child, as her unmarried child under 21, qualifies for L-2 status and can attend school in Oregon. The partner does not qualify as an L-2 spouse because the relationship is not a marriage recognised for immigration purposes, and a common-law relationship, however long, does not meet the definition.
The partner's options are limited: visitor admission for genuine short visits, a student status if they enrol in a program, or their own employment-based status if they qualify for one. Some couples in this position marry before the move, which converts the partner into an eligible spouse who, once admitted in L-2, is employment-authorized incident to status. That is a personal decision with consequences beyond immigration, and it should be made with full information rather than as a paperwork fix.
The engineer's L-1B petition does not change; the question is entirely about who may accompany her.