I've encrypted my disk using the disk encryption option during installation (of Lubuntu) and also used the Home folder encryption option. I wonder whether the latter adds security or if home folder encryption is redundant since I've encrypted the disk.
I'm going to say overkill. You incur a penalty in performance for the decryption twice, while only gaining a marginal increase in security. If an adversary is able to bypass the full disk encryption in some way, by stealing the keys from memory, using a keylogger or just beating it out of you with a wrench. Then breaking any secondary encryption is only going to take a bit more effort, because the same method can be used again.
If only considering Full disk encryption vs a file system encryption. Then FDE is more secure, because a filesystem encryption usually only encrypts the files, so filesystem metadata is still available (number of files, size of files, access data). Depending on the particular system used, the filenames might not be encrypted either.
Sure it increases security, as long as you are using different passphrases for each one.
And just in case one method is found to be flawed (could happen, see shellshock) or you wrote the passphrase on the case or something, there's a "backup" encryption.