Lupa is one of the sacred lukoi words and the title of the chosen mate of a leader of a werewolf pack. Sex appears to be an integral part of the relationship and a lupa cannot be platonic or non-sexual with their ulfric (which is why Sylvie never sought the role from Richard). As ulfrics are usually male, lupas tend to be female, but it's unclear whether a male lupa would be possible for a female or gay ulfric. An ulfric and their lupa are often married in mundane life, but this is not always the case.
It's not necessary for a lupa to also be an alpha, as they gain their status within the pack through their ulfric, but if they also want to be the most dominant female in the pack they need to fight for that status. Even without that, a lupa outranks every member of the pack except for their ulfric, including the enforcers. It's possible for a pack member to acknowledge someone's status as the lupa and a higher ranking member of the pack without acknowledging them as being dominant. Lack of lupa seems to destabilize the pack and lead to eligible pack members competing for the position, even if it's not something that can be won (unless the ulfric happens to be impressed by such things, presumably).
If a lupa becomes disappointed in their ulfric, the lupa can declare themselves as Freyja and challenge the ulfric to prove their worth and to reclaim their place in the lupa's bed if they can.