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No, you do not need a lawyer to complete your advance directive (also called a living will). You may want to consult a lawyer, though, if you make changes to the advance directive form. The form needs to be signed in the presence of witnesses and it is recommended, although not required, that it also be signed in the presence of a notary.
For more information and a copy of Delaware's Advance Directive form, see the Advance Directives section of this website.