As you said you want to remove and eventually reinstall (if I correctly understand your question) I would say, it is okay to do so.
lubuntu-core are metapackge which actually doesn't install anything (those packages are used to pull other packages) and
lubuntu-default-settings is used to set the default settings of Lubuntu, such as default background, theme, icon-theme, keyboard shortcuts and others.
You said, when you wanted to remove
pcmanfm, synaptic said, it will also remove
lxde-core. This is normal since package
pcmanfm is a dependency (you may say required package) for those packages and when you tried to remove it, there is no reason to keep those packages. (Because those packages wouldn't install without pcmanfm).
If you really wanted to reinstall pcmanfm and you have another DE such as Xfce or KDE or Unity (GNOME), I recommend you to switch to that DE and run this command in a terminal to remove and reinstall the packages.
sudo apt-get --purge remove pcmanfm
This will remove pcmanfm, those other five packages with all of their configuration files. Now use this command to reinstall everything
sudo apt-get install lubuntu-desktop lubuntu-default-settings lxde
Note that this command did not explicitly say to install
pcmanfm but that package will be installed as a dependency package of
lubuntu-core which will itself be installed as a dependency of
If you don't have other DE installed, just switch to one of the virtual console by pressing Ctrl+Alt+F1 and execute the commands. To return to the graphical session, press Ctrl+Alt+F7 .
This should help you to reinstall pcmanfm.