The marriage contract ketubah was usually given to the bride and not held by the Synagogue. It is written in Aramaic and not Hebrew and gives the groom and brides father names as well as the couple's Hebrew name.
Unless one of your family retained the ketubah you won't find a copy. They were often lost by the family.

The use of a middle name by a son is usually to honour their dead father but this is not consistent and in my own line my great grandfather used his father's first name as a middle name when his father was still alive.

You won't find birth records pre 1837 civil registration unless among Synagogue records as circumcision records and many such records do not exist as you can see from the Synagogue Scribes Circumcision records which only refer to a very small percentage of the Jewish male population and a specific mohel.

This is not easy research unless you can tie in Lewis to the Isaac Isaacs family line as you are trying to do.