Comment 7 for bug 876945

So according to those logs, lightdm recommends unity-greeter.

***************************************************************************
$ apt-cache show lightdm
Package: lightdm
Priority: optional
Section: x11
Installed-Size: 420
Maintainer: Robert Ancell <email address hidden>
Architecture: amd64
Version: 1.0.1-0ubuntu3
Provides: x-display-manager
Depends: debconf (>= 0.5) | debconf-2.0, upstart-job, libc6 (>= 2.4), libglib2.0-0 (>= 2.28.0), libpam0g (>= 0.99.7.1), libxcb1, libxdmcp6, libpam-runtime (>= 0.76-14), libpam-modules, adduser, dbus
Pre-Depends: dpkg (>= 1.15.7.2)
Recommends: xserver-xorg, unity-greeter | lightdm-greeter
Conflicts: liblightdm-gobject-0-0, liblightdm-qt-0-0
Filename: pool/main/l/lightdm/lightdm_1.0.1-0ubuntu3_amd64.deb
Size: 95592
MD5sum: 8dafd77dc26de0340c651af922f39944
SHA1: 997d17220b291be592f0c70a25be45200fea0ebd
SHA256: 2a7af40723c3112c53742e1127f76f78b31d0fc0c882f594781d0f69c2bbe25a
Description-en: Display Manager
 LightDM is a X display manager that:
  * Has a lightweight codebase
  * Is standards compliant (PAM, ConsoleKit, etc)
  * Has a well defined interface between the server and user interface
  * Cross-desktop (greeters can be written in any toolkit)
Homepage: https://launchpad.net/lightdm
Description-md5: a04ec89b09d7becf8ba288295841fad0
Bugs: https://bugs.launchpad.net/ubuntu/+filebug
Origin: Ubuntu
Supported: 18m
Task: ubuntu-desktop, ubuntu-usb, edubuntu-desktop, edubuntu-usb, xubuntu-desktop, mythbuntu-backend-master, mythbuntu-backend-slave, mythbuntu-desktop, mythbuntu-frontend, ubuntustudio-desktop
***************************************************************************

It looks like that can also be resolved using lightdm-greeter.

***************************************************************************
$ apt-cache show mythbuntu-lightdm-theme
Package: mythbuntu-lightdm-theme
Priority: optional
Section: universe/misc
Installed-Size: 864
Maintainer: Ubuntu MythTV Team <email address hidden>
Architecture: all
Version: 0.9
Replaces: mythbuntu-gdm-theme
Provides: mythbuntu-gdm-theme
Depends: lightdm-gtk-greeter
Conflicts: mythbuntu-gdm-theme
Filename: pool/universe/m/mythbuntu-lightdm-theme/mythbuntu-lightdm-theme_0.9_all.deb
Size: 706860
MD5sum: d60dd5549e31b94a5a2f284a3d6ae520
SHA1: a7b464ebe70c37ab93eb62a589d61cbb5ebf448a
SHA256: 4991972ba230afcd96deb5aa7cd9269240557dd718cdb58396db963ccfd0545e
Description-en: Mythbuntu LightDM setup
 The lightdm greeter theme and configuration
 used for a standalone Mythbuntu installation.
 .
 This package can also be installed on
 other Ubuntu desktops desiring to use this
 theme, but it will replace the LightDM theme.
Description-md5: 367aa8d32815cca27c49c0e62f0c03f2
Bugs: https://bugs.launchpad.net/ubuntu/+filebug
Origin: Ubuntu
Task: mythbuntu-backend-master, mythbuntu-backend-slave, mythbuntu-desktop, mythbuntu-frontend
***************************************************************************
mythbuntu-lightdm-theme doesn't provide lightdm-greeter, but it's dependency lightdm-gtk-greeter does.

I'm unsure why update manager didn't see lightdm-gtk-greeter as resolving the lightdm-greeter dependency for lightdm.