Hello! I didn’t know about this connection so I searched online and while britannia.com only makes a (unsourced) connection between Viviane and Diana’s names, I found that there is a plot connection between them in Merlin Vulgata.
Bruce’s arthurian dictionary describes it like this:
Diana
The Roman goddess of the hunt. According to the Vulgate Merlin, it was her enchantment, given to Dyonas, that caused Viviane (the Lady of the Lake) to be so alluring to Merlin. […] Diana is mentioned several times in Spenser’s The Faerie Queene. She raised the huntress Belphoebe, who became the paramour of Arthur’s squire, Timias.
Unfortunately I didn’t find anything about the specific plot you mentioned! but maybe someone out there knows more!
Arthurian Legends 