When using exec, you normally have to enter the full path to the command you execute. So if you change your command into
exec { 'chown':
command => '/bin/chown -R vagrant:vagrant /var/lib/php/session/',
path => '/bin',
user => 'root'
}
it should work imo.
However, it depends a lot how you install your application. If the setup/start of the application is also managed with Puppet, you can also manage the directory you're interested in with Puppet, like this
file { "/var/lib/php/session" :
ensure => directory,
group => "vagrant",
owner => "vagrant",
recurse => true,
}
before you start your app. This would be much more the Puppet way, as you manage a reource then instead of executing commands. However, normally /var/lib/... should not be owned by someone other than root.
So you should maybe look into how your app is started and make it start with another user or as root. If it is started with an exec, you can add an additional property
user => root
to it and that should also do the trick.