There are a total of 68 performances of 60 or more points in NBA history. Fourteen of them had Lakers players as protagonists. Despite WIlt Chamberlain being the king of the high-scoring games with 32 of them (check the complete list), he only did it twice as a Laker.

Elgin Baylor had four 60+ games, including one of the only 2 performances of this kind in the playoffs in NBA history (the other: Michael Jordan with 63). His 61 points are still the NBA Finals record.

Kobe Bryant had six 60-point games, including his famous 81. Kobe, Baylor and Chamberlain are three of the 4 players in league history who did it more than once (the other one is Michael Jordan, 5 times)

Shaquille O'Neal, Jerry West and George Mikan did it once each.

Los Angeles Lakers History: Players with 60-point Games
Points	Player	Team	Opponent	Date
81	Kobe Bryant (1)	Los Angeles Lakers	Toronto Raptors	1/22/2006
71	Elgin Baylor	Los Angeles Lakers	New York Knicks	11/15/1960
66	Wilt Chamberlain	Los Angeles Lakers	Phoenix Suns	2/9/1969
65	Kobe Bryant	Los Angeles Lakers	Portland Trail Blazers	3/16/2007 (OT)
64	Elgin Baylor	Minneapolis Lakers	Boston Celtics	11/8/1959
63	Jerry West	Los Angeles Lakers	New York Knicks	1/17/1962
63	Elgin Baylor	Los Angeles Lakers	Philadelphia Warriors	12/8/1961 (3OT)
62	Kobe Bryant	Los Angeles Lakers	Dallas Mavericks	12/20/2005
61	Kobe Bryant (2)	Los Angeles Lakers	New York Knicks	2/2/2009
61	Shaquille O'Neal	Los Angeles Lakers	Los Angeles Clippers	3/6/2000
61	Elgin Baylor (3)	Los Angeles Lakers	Boston Celtics	4/14/1962
61	George Mikan	Minneapolis Lakers	Rochester Royals	1/20/1952 (2OT)
60	Kobe Bryant	Los Angeles Lakers	Utah Jazz	4/13/2016
60	Kobe Bryant	Los Angeles Lakers	Memphis Grizzlies	3/22/2007
60	Wilt Chamberlain	Los Angeles Lakers	Cincinnati Royals	1/26/1969

Notes:
(1) Second best ever in NBA history.
(2) Madison Square Garden record
(3) In the playoffs / NBA Finals record.