Homebrew issues error while calling 'brew update'
The index.lock file which is located in a directory which might need root permission to modify it or its files. You can change the permission of a directory using the chmod command. 

This is what you can do:
sudo chmod -R +w /path/to/directory

A good choice for directory in this case might be '/usr/local/Library/Taps/'

The -R option will recursively execute the command on sub directories and files.

The +w option will add write permission to the mentioned directory or file for everyone.

Good Luck. ;)