The judge in the Dover case (Kitzmiller et al. v Dover Area School District et al.) applied the Lemon test because both sides agreed to it However, the judge said:
After a searching review of Supreme Court and Third Circuit Court of Appeals precedent, it is apparent to this Court that both the endorsement test and the Lemon test should be employed in this case to analyze the constitutionality of the ID Policy under the Establishment Clause, for the reasons that follow.So your problems with the Dover decision go way beyond Lemon.
The Lemon test is a problem all on its own. The Supremes have commented on it several times. The Dover decision may have been a good opportunity to clean it up, but it appears it'll be another case.