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http://www.tevu-darzelis.lt/vaiku-vardai/liveta/

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This Lithuanian name site (Lithu-name-ian, if I may) speculates it is from Liva, a short form of Livija, which I think is slightly more credible, and there appear to be Lithuanian bearers of the name Livija upon a Google search.

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http://www.vardai.org/vardo-reiksme/liveta/

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This site also connects Liveta to Livija.

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Livija appears to be the Lithuanian feminine form of Livius.
http://www.behindthename.com/name/livius