I do not have access to Brian's 1861 census index at present. Where and, with whom, was Martha living in 1861?
On the IGI, I found no Martha christenings in the Andreas parish around 1816-1820.
In fact, I suspect that many of the Andreas birth records for those years may be missing. For example, in the five year period 1818-1822 there are 83 marriages in Andreas on the IGI but only 31 christenings, about 20% of what one would expect.
There is a Martha Corteen christened at St. Peter Liverpool on April 8, 1818. Her parents are David Corteen and Sarah. David Corteen married Sarah Shaw at St. Nicholas Liverpool on March 4, 1816. A slight possibility is that she was born in Andreas, christened in Liverpool and returned the IOM (parents died young?) to live with relatives. This does not explain where the name Lord comes from.
Also there is a Martha Cottier in the 1861 census. She was also born in Andreas, but was aged 39.
Note also from Brian's burials: Martha Morrisson December 24 1907 age 92 (= DOB 1815, a 3 year gap, but this corresponds to her age of 86 in the 1901 census)