Italian uses the third person feminine by following Spanish usage of usted. It simply never developed a special pronoun, which is reasonable as Italian very rarely uses the pronoun at all (e.g. Cosa desidera?, Si accomodi, prego etc.) and prefers to express the person via verbal agreement. It used to alternate with the voi form (2nd person plural), but it displaced it after WWII as the latter had a strong association with the Fascist regime. There is also a loro (3rd person plural) form but it's nowadays basically confined to satire, as it is perceided as comically stuffy.
The German Sie is not a 3rd person singular form - it is a 3rd person plural form (as can be seen from the verbal agreement) and so it has more to do with the Italian loro than with lei. It has a similar origin to usted in that it comes from an ellipsis of Euer Gnaden, which means something similar to your grace but it is plural (and so requires the 3rd person plural form). It displaced the Ihr form (2nd person plural) in the nineteenth century, although I'm not sure what prompted it.
The similarity with the feminine 3rd person pronoun sie in the German language is completely accidental and has, as best as I can tell, no relation with the Italian lei or the Spanish usted.