I searched and I cannot find in our Constitution where it says we have to seperate church and state. Just something about Congress shall make no law promoting one religion over another.
Seperating church and state is exactly what not promoting religion means. If the state where to pass a law that says you have to swear by Jupiter that you are telling the truth in court, that is favoring the roman religion over other religions. The only way to keep the state from promoting a religion is to keep church and state seperate.
The court has generally interpreted that part of the constitution such that atheism is considered a religion for purposes of establishment. That means that the government can not promote religion in general nor can it promote non-religion in general.
So then what about those court rulings that say religious stuff in the government is Unconstitutional?
The principle here is that for the government to favor one religion over another in anything is an illegal establishment of religion.
Notice that it is not all religious stuff in the court room that is illegal. Only presentations that favor one religion over others that are excluded. It's still legal to swear to tell the truth on the bible, as long as you are allowed to not do so if your not a christian. Many courts are littered with various religious symbols, usually Greek/Roman or Christian, as long as such symbols are just artwork there isn't a problem.
Ex-Judge Moore's monument and similar displays of christianity are illegal because they are intended to place christianity in a favored place. Look at this website [link|http://www.morallaw.org/monument.html|MoralLaw.org] which has a description of the monument. It makes perfectly clear that the point of the monument is to claim that the US legal system is derived from and secondary to the christian God's rules.
As for the statues of Lady Justice, it's hard to say how they would be considered if the Roman and Greek faiths where not dead. The statues do not if fact depict any specific Roman or Greek figure, but historically it was derived from various goddesses. I suspect that the courts would hold that it is a representation of idealized justice that does not embody any specific religion and would be considered legal.
Jay