Cox, a 53-year-old businessman from Dunboyne in Ireland, suffered serious head injuries in an incident outside Anfield prior to the Champions League semi-final first leg on April 24.
Attending the match with his brother, it is believed Cox was hit with a belt.
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A jury of six women and six men returned a majority not guilty verdict in relation to the charge of GBH after nearly nine hours of deliberation at Preston Crown Court.
Lombardi, 21, had admitted to a lesser charge of violent disorder prior to the trial, for which he has been sentenced to three years in prison.
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