I do not believe there is any connection between the Lady of the Lake and the Lady of Shalott, other than that they are both placed in the same literary time period.
The Lady of the Lake appears in Thomas Malory's Morte d'Arthur, from the 15th century. The Lady receives the sword, Excalibur, from Sir Bedivere after Arthur is mortally wounded.
"The Lady of Shalott" is a poem written by Tennyson in the 19th century. It features a Lady trapped in a castle by a curse, a short ways from Camelot. Sir Lancelot appears in the poem.
Both literary works are placed in the time of King Arthur and of Camelot. But there isn't any other connection between them.