Emily is clearly not healthy, either mentally or physically, and unless she gets healthy we will never know the full extent of her eating disorder or her issues. She is clearly not wanting to face them, hence the lying, though I genuinely think at this stage she is also lying to herself more than just her viewers. Considering who her mother is, and that she is a child psychologist, I hope she is helping Emily.
However, it looks like she has always had issues with eating, so its surprising, that it has escalated to this point. Maybe thats why the family pander to her, as they know anything more will hurt Emily even further?