Final answer:
Emily appears to be suffering from Major Depressive Disorder (MDD), given her symptoms and personal history, which align with the characteristics of this mood disorder.
Step-by-step explanation:
The most likely diagnosis for Emily, considering her symptoms of persistent sadness, lethargy, and difficulty concentrating, alongside the context of an abusive relationship and a difficult upbringing, would be Major Depressive Disorder (MDD). MDD is characterized by a severe and pervasive feeling of sadness that goes beyond normal grief or feeling 'blue.' It includes physical symptoms such as weight loss or gain, loss of interest in activities, and disrupted sleep patterns.
Given Emily's history and current state, these symptoms are reflective of depression, rather than conditions such as antisocial personality disorder, bipolar disorder which involves mood swings, or obsessive-compulsive disorder that includes repetitive thoughts and behaviors.