If he bought the house then there would be record held in general registry (or manx Museum - this period is around when the records switch) - however it is more likely he rented the property - thus suggest you can look in newspapers for the period before his sons started for a house to let (I understand that some of Manx Newspapers of this period are also on microfilm at UK National newspaper library Collingdale N. London.
Derbyhaven is small (and still smaller in 1901 - there is a 1870 plan at www.manxnotebook.com/gazateer/dhaven.htm - you could try matching 1901 entries to properties. Unless there is a record of some house name, 'Lomas Derbyhaven' would be a perefectly adequate postal address - there are only two big houses of that period I can think of - on the corner of the road leading from the school.