Herbert Dalziel was the son of Thomas Bolton Gilchrist Dalziel (1823-1906), who was the brother of George Dalziel (1815-1902), Edward Dalziel (1817-1905) and John Dalziel (1822-69), the brothers who formed the wood engraving firm, the Brothers Dalziel, initially set up by George in 1839. Herbert's brother Owen was also a painter.
Herbert Dalziel, who specialised in flower, figure and landscape painting, became a member of the New English Art Club in 1887, the year before Whistler exhibited with the group. He was active in exhibiting between 1881 and 1902 and showed at the Royal Society of British Artists, a society that had elected Whistler its President in June 1886. He also exhibited at the Royal Academy, Grosvenor Gallery, New Gallery, Dudley Art Gallery, Royal Institute of Painters in Water Colour and Royal Institute of Oil Painters in London, as well as at the Royal Hibernian Society in Edinburgh, Royal Society of Artists in Birmingham, Walker Art Gallery in Liverpool and Manchester City Art Gallery. H. Dalziel was amongst those proposed invitees to a dinner organised by W. C. Symons to congratulate Whistler on being made an Honorary Member of the Royal Academy of Munich, a dinner which was to be held at the Criterion in Piccadilly on 1 May 1889.