If you don’t have that file, then there’s something seriously wrong with your installation. /etc/mkinitcpio.conf is essential for rebuilding the initramfs whenever the kernel gets updated, and without an initramfs you cannot boot ─ it contains all your needed driver modules.
Try reinstalling mkinitcpio. 
sudo pacman -S mkinitcpio
I’m afraid I can’t help you with the lightdm problem, though. 