This is a pretty baseless speculation on my part but I wanted to put out a wild idea: I think that, before being fully intergrated into Arthur's mythology, Lancelot's tale was originally a revenge story of his mom.
Reading off of Lanzelet and comparing it to Vulgate Lancelot, there are some common beats that may point to a particular plotline:
A king and his family get ousted (by Claudas in Vulgate, by the King's own subjects in Lanzelet). The king dies while the queen mother and newborn son (Lancelot) flee.
The newborn son gets taken by a fairy while the queen wasn't looking
The son grows up to be an overly eager warrior that dashes off to his adventures... all while not knowing his name.
At a pivotal point - usually defeating a great foe and seizing his keep (Iweret in Lanzelet, Dolorous Gard in Vulgate) - the young man finally learns his name: Lancelot.
From there, it gets murky as this where different stories go in different directions but a popular plot might be the Guinevere Abduction theme, which some other heroes have done.
Eventually though, Lancelot goes on to retake his kingdom and overthrow his family's usurpers. He reunites with his mother and the story ends.
This way, it looks like a classic revenge story with the long lost prince coming of age and proceed to take back what's rightfully his.
I came to this conclusion because I was contemplating about how one of Lancelot's most defining aspect (outside of his love affair) is him being seized and raised by a fairy and how a hero could condense out of the "Child-Stealing Fairy" motif
But then I noticed that Lancelot eventually reunites with his birth mother at some point in the stories:
(Source: Vulgate Cycle - Lancelot pt. VI)
(Source: Lanzelet, by Ulrich von Zatzikhoven)
This is the speculative part: I believe Lancelot's birth mother - Elaine/Gostanza/Clarine/whatever - was originally a sorceress. I think Lancelot's hypothetical "original" tale was that of a fallen witch queen who rears her son to be her instrument of revenge and defeat their enemies.
I think the "kidnapping fairy" was conceived to absolve the mother of the charge of wielding sorcery when tastes changed, when it was no longer culturally acceptable to have a scheming witch as the protagonist's mother.
Hypothetically, the proto-story would go like this:
After being overthrown and her husband killed, the Queen escapes with her son and using her magical powers, creates a hiding spot to lay low as she raises her son to manhood
The Queen hides her son's identity and heritage to protect him from being assassinated before gaining enough strength to oppose their enemies in public, all while providing her son magical aid from time to time.
After achieving enough renown, gain allies and receiving knowledge of his heritage, Lancelot proceeds to take back their kingdom (probably getting a love interest along the way) and in the end, Lancelot triumphs, the mother comes out of hiding and they all live happily ever after.
So basically, the Lady of the Lake is a literary double/surrogate of Lancelot's real mom so that she can remain respectable for the medieval reader's sake while also keeping a mystical parental figure in Lancelot's life.
