I can't read the text, but this site, which discusses what appears to be this icon, independently of the Slidell controversy, reports that the text corresponds to John 7:24 ("Judge not according to the appearance, but judge with righteous judgement") and Matthew 7:2 ("For with what judgement you judge, you shall be judged"). This is indeed more courthouse-related text than what I understood the quote to be earlier. [UPDATE: The ACLU of Louisiana was kind enough to send me a more readable version, and Sasha, who knows how to read Old Church Slavonic -- which differs enough from standard, even pre-1918 standard, Cyrillic Russian that it requires special skill in reading -- was kind enough to transliterate it into Russian. With this, he and I can confirm that the text is a combination of John 7:24 and Matthew 7:2.]
Still, the bottom line seems to me to remain: To the extent the text matters, it's New Testament text; to the extent the text should be ignored, since the overwhelming majority of observers won't understand it, it's apparently a depiction of Jesus. In either case, it seems unconstitutional even under Justice Scalia's proposed test for a court to display the work in this context, as a standalone work in a court house with the caption "To know peace, obey these laws."
UPDATE: Thanks to commenter Paul Lukasiak for a pointer to the picture as it appears in context: