I use Synaptic as my package manager and right-click for the "reinstall" choice for each package. If you check off both at the same time, the system will figure out the necessary precedence as to which should be done first.
Otherwise, for lightdm, you can use the line command
dpkg -S $(realpath $(which lightdm) )
which will report the package name (field left of ":")
lightdm: /usr/sbin/lightdm
... and again, for plymouth ...
dpkg -S $(realpath $(which plymouth) )
which will report
plymouth: /usr/bin/plymouth
then reinstall both using
sudo apt-get install --reinstall plymouth lightdm
Single-line apt-get commands should have the smarts to install in the necessary logical sequence. I happen to know that lightdm "manages" the use of "plymouth", so I placed them in what I believe is the necessary precedence list for install, but I truly believe that it would figure it out on its own if necessary.
There is this other discussion where the "infrequent" occurence of no package reported using the "dpkg" search function does occur. That is all I am going to say here about that.