add i3lock.pam (installed as /etc/pam.d/i3lock) which includes 'login' (Thanks Семён)

[i3/i3lock] / i3lock.pam

#
# PAM configuration file for the i3lock screen locker. By default, it includes
# the 'login' configuration file (see /etc/pam.d/login)
#

@include login