Emily Greaves was the sister of Henry and Walter Greaves, who were pupils and followers of JW. It is not entirely clear if she was actually known as 'Eliza' since in the census of 1881 there are only two Greaves sisters listed, Emily and Alice. Alice ('Tinnie') Fay Greaves and 'Eliza' modelled for JW. Their father Charles William Greaves was a Chelsea boat-builder and waterman.
The Greaves lived a few doors from JW, at 9 Lindsey Row. JW on occasion would invite the whole family to dinner (#11454).
According to Walter Greaves, Elizabeth and her sister made the carpet of black and white tape which JW used for Harmony in Grey and Green: Miss Cicely Alexander (YMSM 129). At some point in the 1870s JW asked Walter Greaves not to paint Eliza wearing a blue dress, 'for you know Walter my picture of little Miss Leyland in blue cashmire [sic] and velvet [The Blue Girl: Portrait of Miss Elinor Leyland (YMSM 111)] - in short, the arrangement in blue - you know how jolly it is - and of course I shall paint it directly I have time' (#11494). However, Walter did paint the picture he had proposed of the 'Blue Girl'. Walter also painted and etched a number of pictures of his sisters.
UK census 1881, from http://www.familysearch.org (accessed 2004); Young, Andrew McLaren, Margaret F. MacDonald, Robin Spencer and Hamish Miles, The Paintings of James McNeill Whistler, New Haven and London, 1980.