You probably know all this.

William Henry Robinson, son of James & Alice Robinson born in Stretford Lancashire c. 1845, married Elsie Lawton in the March quarter of 1871 volume 8d page 477.
Elsie Lawton does not appear in any IOM record that I can locate.
Her age varies from 27 (poss.22) in 1871, 32 in 1881, 43 in 1891 and (named Alice) 54 in 1901.
Alice Lawton could be the daughter of Thomas Lawton and Hessy Cowin chr. March 14 1841 and who, aged 10, is living in Braddan in 1851 with Agnes 7, and Esther (68) and William Cowin (72).
Alice Lawton 20 is in the IOM 1861 census in Lezayre. This confirms what Len suggested.

The options seem to all negative. Death, divorce, abandonment, etc.
Sometimes there is an indication on a marriage certificate as to whether a father (Walter) is deceased.
With a name like Smith, it will be a long slog through death records, but you could start with Cheshire in Macclesfield.
Good luck, I hope you find something.