I have read the following sentence in an Italian learning tool:
Voglio che ci lavori lui su tutto. (= I want him to work on everything / I want that he work on everything)
What does "ci" mean here ?
In this sentence, particle "ci" has the meaning of "su tutto". It is used in a pleonastic way because the sentence of your question contains a "dislocazione a destra", a construction typical of oral speech which is explained in detail in this answer.
As in this example given in that question
Non ci sono andato, a Venezia
which comes from the book Grammatica dell'italiano adulto by Vittorio Coletti, the sentence has a complement ("a Venezia" in Coletti's example, "su tutto" in your sentence) that goes after a complete clause ("Non ci sono andato" in Coletti's example, "Voglio che ci lavori" in your sentence) and which is anticipated in this clause by particle "ci".
In this case "ci" is pleonastic, which is why Google ignores it.
This sentence construction ("ci lavori lui" rather than "lui lavori") stresses the fact that the speaker wants him ("lui") to be the one doing the work.