If you look on Synagogue Scribes- Great Synagogue Offertory Book ( GSOFa)-Henry Roche you will see 2 records- Benjamin Lyon Phillips father Zeeb plus other related records; Joshua Lyon Phillips father Isaiah plus related records. You will also see on Cemetery Scribes Joshua Lyon Phillips ID 1287 =Elizabeth Harris and on JewishGen UK Data base Insurance Policies- Benjamin Lyon Phillips Manchester warehousemen 38 Minories with joint policies linking Joshua Lyon Phillips and Coleman Lyon Phillips plus Joshua Lyon Phillips victualler French Alley Paternoster Row Spitalfields 1822-23 jointly with Benjamin and Coleman.

What I can't see are any records which link these lines to the James Phillips widower=Mary Stokes marriage 1790 or to John Phillips b circa 1798- the above are all Jewish whereas your John Phillips and the James Phillips who married in 1790 are not.

Where to look next?
Phillip