I did some research on Robinson Families on the IoM around this period and did not come across the name Beavily (? is this the correct spelling ) nor if I recall a doctor Robinson - most of what I have is at http://www.ee.surrey.ac.uk/Contrib/manx/famhist/families/rbson.htm
The Lyons name is not manx and not that common
There was a Lyons Philip M. surgeon, Brause(Andreas) in 1846)
and in Santon MI's is
Jane Lyons, daughter of Samuel Lyons of Bangor in Ireland and Margaret Lyons alias Brew, his wife, departed this life the 12 April 1831, aged 15 years.