Unfortunately, the best answer I can give, seems to be that none of the other Drow deities, appear to have any alignment like that.
Other than Lolth and Elisatree: Zinzenna is Chaotic Neutral (3e portfolio: chaos, luck, trickery). Kiaransalee is Chaotic Evil (3e portfolio: Undead, vengeance). Vhaeraun is also Chaotic Evil (Drow males, evil activity on the surface, thievery). Even Ibrandul, an underdark but not drow deity, is chaotic neutral (Caverns, dungeons, skulks).
None, would fit specifically as a lawful good diety, if that is compulsory.
But alternatively: The drow as a society, canonically have a lot of slaves. Including those from the surface. Kidnapped during raids.
I see from a comment, that they're fresh from the underdark your PC. But, depending on their experiences: that does not necessarily rule out, that they could have met someone in the Underdark who's from the surface. Meaning they would be familiar with the gods there.
So potentially, if you're open to that possibility: you could have a surface deity as the patron of choice. A more likely example of them, could perhaps be the Lawful Good surface deity Ilmater (Endurance, Martyrdom, Perseverance, Suffering).
Ilmater is explicitly said by his lore, to be popular amongst slaves. Making it a high possibility that surface-born people, who were abducted to be slaves in the underdark, could worship him. Here is a quote from the forgotten realms wiki:
His faith was popular among the poor in big cities, and with serfs and slaves
Which would make him a deity "present" there, even if not from/of there.
Ilmater could potentially appeal, to a radical/outcast lawful good drow (especially if they're male too) with his sort of purported ideology:
He was the god of those who suffered, the oppressed, and the persecuted, who offered them relief and support, encouraged them to endure, and who encouraged others to help them,
Although, of course, this would most likely require some form of interaction with these slaves. Or at least one, to have learned about the deity. As they would have had to have told the character about him somehow.
So, whether that's compatible with the character's backstory is also important to consider.
Unfortunately this is the best answer I can give, to hopefully help.
(Citation: all quotations are from the forgotten realms wiki: which also cites specifically where they got this information from.)