find /nas/content/live/lifeofaserver/vhosts/ -perm 777
… or to same the results in a file:
find /nas/content/live/lifeofaserver/vhosts/ -perm 777 > /root/files.txt
Also, if you want to only see the files with some permission you can use:
find /nas/content/live/lifeofaserver/vhosts/ -perm 777 -type f
…. or directories:
find /nas/content/live/lifeofaserver/vhosts/ -perm 777 -type d