Have Mental Health Questions? Ask a Psychiatrist Online
If she is refusing treatment, there is little you can do -just encourage her and offer perhaps to go in with her for support to the first session.
Unless she presents imminent danger to herself or another, you won't be able to commit her involuntarily or have her get the needed treatment. If in a crisis/posing a threat, you can try to have her involuntarily committed to a crisis center and kept there for an eval for up to 72 hours. This will depend on the state you live in. Usually the probate judge handles the issuing of the affidavit order and the sheriff dept picks her up.
You may want to try to find out why the resistance on her part (some people with eating disorders do not see anything wrong with that) On the other hand, the lying is something that she has to also want to work on.
Perhaps a family intervention in the home with others can be something you could explore.