While both mythical ladies relate to Arthurian Legend, it depends upon the author as to how they are portrayed.  For example, the Lady of the Lake is normally characterized by authors as strong and controlling.  She is responsible for presenting Arthur with Excalibur (his sword) and is sometimes credited with kidnapping Lancelot when he was a child.

In contrast, Tennyson's "Lady of Shalott," is tragic and sympathetic.  Instead of living in a lake, she lives in a river and dies before she can actually reach Camelot.  She does not enjoy the power and freedom that the Lady of the Lake possesses.

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.