I argue on the evolution side in this debate. I'm convinced that evolution occurs and I'm the result of biogenisis and 3 billion or so years of evolution and God does not exist.
However.
I have done some research into the original meaning of the Constitution and I think you are completely right about Lemon. The individuals who wrote the First Amendment and ratified it from at least a few states went home to towns that had legally required tithes to the local state church. By 1790, probably all states allowed denominations other than the official state church, but that did not let non believers get out of the tithing law. Tithes from them went to the official church. Tithes from members of other churches went to those churches, but each of these churches had to be chartered through the state in order to accept the money. This completely wrapped up state government with church business and the practice didn't disappear until around 1820.
The First Amendment was specifically directed at what the National Legislature could, and could not do.
The argument is made that the 14th amendment, which guaranteed that all "Rights and Privileges" granted to citizens under the US constitution changed the scope of the First Amendment, but that is nonsense. The 14th was passed after the Civil War for one reason. A few southern states were claiming that the rights of the US Constitution did not apply in the states (toward blacks in particular). That was a stupid argument, because if the Bill of Rights did not apply in the states, then where did it apply? In Washington DC? So the 14th amendment is completely redundant and did not change the meaning of the First Amendment, and the First did not apply to what state and local governments could do.
The First Amendment does not directly grant any rights unlike the Second, which grants a right of gun ownership. The First is specifically limited by its wording to limiting what the federal government can do.
One mistake many readers make is reading the "Bill of Rights" from start to finish, which makes the clause "The Congress shall make no law" appear to apply to all subsequent amendments. But the "First" Amendment was not the first amendment sent from the Congress to the states (I think it was the third), but was merely the first amendment ratified. So those magic words "Congress shall make no law" are only relevant within that amendment. Other amendments do not contain those words, so the argument that the First grants rights like the other amendments is bogus.
Another proof that this interpretation is correct is that many states subsequently wrote their own Bills of Rights that duplicated items in the First. Why would they need to if the First applied to the actions of the local government?
I don't think there's any way in h@ll that any court today will interpret the First in the way it was intended by its writers and ratifiers. For one thing the press would get awfully nasty about the idea that it does not have an absolute right to print what it wants.
I think we should interpret the Constitution exactly the way it was intended by it's writers and ratifiers, otherwise why did we bother to write it? That includes limiting the First to limiting the Congress only. But I also think we should amend the First Amendment to actually mean what most people today think it means, explicitly including the words "separation of Church and State", in honor of Jefferson who wrote them.
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