Avram, she doesn’t need to light to know that it is Shabbos. And, more importantly, it is Shabbos for her whether she lights or not, and she’s still obligated in Shabbos. If she doesn’t have a halachic marriage, she isn’t an eishes ish or married, and she doesn’t have the obligations of an eishes ish.
Again, I’m not being a proponent of this idea, merely explaining it. A major problem with the idea is that if they’re not halachicly married they are sinning each time they’re together. [Though that sinning is of a lesser nature than the proponents of this are concerned may occur later if they are halachicly married.] Though, Rav Moshe (unlike Rav Henkin) holds non-Orthodox performed marriages are, indeed, not halachicly valid.