Sorry no Dun/dunns in Lindean. Only 6 readable in the 1960s with names Soott,Henderson.Lee, Elliot,Ingles, Dickson,Brydon and Ker.
In the Auld Kirkyard Selkirk there is a Major John DUN died 1845 wife Dorothea Henderson. Another George DUN died 1736 aged 78 with a daughter Margaret. also a John DUNN died 1873 aged 58yrs wife Hyndmer Rutherford Hewat with a son Thomas and dau Hyndmer.
I have checked my index for the old cemetery by the Old Town Galashiels and found Euphemia DUN born 29-3-1816 died 23-1-1895 but i expect you have that one.