You need to buy the marriage cert from the Registry, and this will give you the fathers' names and occupations.
Marriage: LEWTHWAITE, Alexander, 4 May 1895, D, CHRISTIAN, Sarah.
[www.iomfhs.im/lawsons/marriages/l_mar.html]

If you are not in the IOM you can write to them (see "Contacts") at www.gov.im/registries/general/civilregistry/

Sue