Here's a brief summery of why the lunar Sabbath teaching doesn't pass the test of Scripture:
1) Lunar Sabbath fails the “Bone Structure” Test. The first Sabbath was 3 days after the moon was created (since the moon was created on the 4th day of the Creation Week). Clearly the first Seventh-day Sabbath on earth was not determined by the moon. (For more information on “Bone Structure” as a vital part of effective Bible study, see the Lighted Way Ministries, Study Guide #1, readable online at https://www.lightedway.org/html/Doctrine_Studies/Lesson_1.pdf)
2) Lunar Sabbath teachings cite massive calendar changes... which are invalid... Christ kept the same day Sabbath that the Jews kept, demonstrating that Saturday was the Sabbath. As it says in Hebrews, had there been another day of rest, He would have said so (Heaven only keeps Heaven's Days). So all calendar changes prior to Christ are invalid to proving Sabbath-changes (for they did not affect Sabbath).
3) Lunar Sabbath is not consistently 7 days... If Sabbaths are governed by the moon phases, Sabbath is no longer consistently the Seventh-day Sabbath. At the end of each lunar cycle, there is a 9-10 day period from one lunar phase to the next. This means that the last week of the month, if Lunisolar Sabbath is true, is not seven days - thus it is not consistently the Seventh-day Sabbath, if Sabbath were determined by the moon phases.
4) Lunar Sabbath days are not consistently the Sabbath, in the Bible Record... There are any provable cases in Scripture where the weekly Sabbath DIDN’T fall on the 8th, 15th, 22nd or 29th. Even one provable case disproves the Lunisolar theory. There are two!
5) We will to look at the history of keeping the Sabbath to see whether it was done by the moon phases or by a continuous count.
6) We will examine the Seventh-day Sabbath to determine whether there is enough evidence to show that “Saturday” is indeed still the 7th Day.
7) The Pentecost count includes seven Sabbaths AND fifty days. The Pentecost count doesn't work with the weekly Sabbath being determined by the moon phases... This is because there is a 9-10 day period at the end of each lunar cycle... And even one 9-day "week" following 4 weeks, throws off the Pentecost count, making it impossible.
Next, we will study how to make a Biblical calendar (determining the timing of the Feast Days) - as the Feasts are a subcategory under the Sabbath Commandment.
