I just wish I could find ONE record of them all actually emigrating!Me too, goldie61
This family is quite elusive considering there were quite a few of them and that they appear to have run shops/businesses, and may have been reasonably well-known in the Ballarat area.
The immigration shipping lists held by the Victorian government begin in 1852 so I suppose there's a possibility that they arrived before those records began. The other avenue which may give a clue is to buy the image of Eliza's death certificate.
You may already know all this so I apologise for the repetition if you do. Victorian BMD records are very informative (so long as the informant is knowledgeable/truthful. This is the information asked for:
Deaths
Date and place of death;
name and surname;
occupation of the deceased;
sex and age;
cause of death, duration of illness, medical attendant by whom certified and when he last saw deceased;
name and surname of parents (if known) including mother's maiden surname
signature, description and address of the person who gave the information;
signature of deputy registrar, date and where registered,
when and where buried,
undertaker whom certified, name and religion of Minister, or names of witnesses of burial;
place of birth of the deceased and
how long he or she resided in the Australian colonies or states (stating which), name of spouse, place of marriage, age at marriage;
names and ages of children of the deceased.
Looking at the index entry for Eliza, the informant knew her parents' and spouse's names so it would seem likely that the informant might also know how long Eliza had been in Australia/Victoria. The index entry for Lewis shows less information - not uncommon for those who die in an institution.
John Barratt Hall's index entry seems to be complete also and his death is nearer the probable date of immigration.
Images of Victorian historical bmd records can be purchased for $AU20 and the3 image is emailed to you directly.
https://www.bdm.vic.gov.au/research-and-family-history/search-your-family-history