The commas are neccessary. The phrase "whose father is a lawyer" is a
parenthetical phrase, which means that it interrupts the sentence "John is my best friend" in order to add information about John.
If the information contained in such a parenthetical phrase is not essential to the meaning of the phrase, it is set off by commas. If not, no commas should be used:
John who saved my life is my best friend.
An article about commas is to be found at
http://en.wikipedia.org/wiki/Comma_(punctuation)