I'm paranoid when uninstalling apps because I'm under the impression that uninstalling them directly without using the "Clear Data" function on the app's page first will result in leftover files somewhere in the phone's system. So to finally get an answer, I'm asking here, in Lollipop, when I uninstall apps directly, do I not need to do "Clear Data" first?
Force stop → clear data → uninstall is the same as uninstalling app directly as far as removing app data is considered. It's just an extra step with no added benefit.
Force stop option is primarily to troubleshoot apps when they misbehave
Either method does not guarantee removal of all app data - you would need root to ensure that. See Can a app store data beyond uninstallation?