Sorry, I thought by "LXDE", you meant the desktop. The lxde package installs lxde-core, lxappearance, lxinput, lxsession-edit, lxshortcut, gpicview, lxterminal, lxmusic,
leafpad and xarchiver. To get lxdm, the lxde-desktop display manager (log-in manager), you need to install it seperately. Gdm must have been the default display manager already on your computer. It should work fine with lxde but it is much heavier than lxdm.