The article below and the study it cites makes a strong argument for allowing non-citizen jurors. According to the article, in criminal proceedings, non-citizens face higher sentences than those who are citizens. The article goes on to say that undocumented non-citizens fared even worse. This article and the study give support to the bill that Governor Brown vetoed last year which would have allowed non-citizens, who were lawfully in the United States, to serve as jurors.
I would also note that allowing non-citizens to serve is not a new concept. For example, England, for close to 500 years, (the practice was eventually abolished by the Naturalization Act of 1870) permitted the jury de medietate linguae, or “jury of the half tongue.” In a jury de medietate linguae a non-citizen defendant was allowed the right to request that half of the jury consist of non-citizens. The practice which has been used in the United States, although not for quite some time, helps non-citizens receive fair treatment under the law.
New Republic: Juries Dole Out Harsher Sentences to Non-Citizens