Lin, in his second NBA season and first with the Knicks, was thrust into the starting lineup for the first time in his career last Monday due to injuries that have hit the team.
The point guard scored 28 points in his debut as a starter against Utah and followed that with his first career double-double Wednesday against Washington.
His 38 points Friday were the most he has scored in any of his 42 NBA appearances.
New York won its fourth in a row, taking the lead early in the contest and never relinquishing it. The Knicks led by as many as 16 points in the final period.
Iman Shumpert added 12 points and Jared Jeffries had 11 for the Knicks, who put together their first win over the Lakers in five seasons.
Kobe Bryant led the Lakers with 34 points. Los Angeles has lost three out of four and is 2-3 on a five-game road trip that concludes Sunday in Toronto.