Siddal modeled for this painting, A Pet, by Deverell (exhibited 1853). The painting depicts pet birds surrounding Siddal in a garden setting. In an interesting article that uses this painting as a starting ground, Elaine Shefer explores the idea of birds and pets in comparison with the relationship between Siddal and Rossetti.1 Shefer analyzes different Pre-Raphaelite paintings, as well as poetry by Siddal and Rossetti, to show how the model was like a "bird in a cage" in her relationship with the painter. Undoubtedly, Siddal had a very sad life (which ended in a purported suicide). Some really fascinating aspects of Shefer's argument comes at the end of the article. For example, she includes discussion of how Rossetti was haunted by the voices of birds after Siddal's death; on at least two occasions the birds "spoke to him accusingly, once with the voice of Lizzie."2This is a really interesting psychological analysis of the relationship between two well-known figures from 19th century art. I haven't found a plethora of scholarly analysis on the Pre-Raphaelites (with the exception of a few writings, like those done by Griselda Pollock). However, this article by Shefer is a nice psychological study that is well-supported with social-historical evidence.
1 Elaine Shefer, "Deverell, Rossetti, Siddal, and 'The Bird in the Cage'," The Art Bulletin 67, no. 3 (September, 1985): 437-48.
2 Ibid., 446.