Combine lemon juice, mustard, and egg yolks in a medium bowl, stirring well with a whisk. Gradually add oil, about 1 tablespoon at a time, stirring with a whisk until each addition is incorporated and mixture is thick. Stir in salt and pepper.
Combine 1/2 ounce dried morel mushrooms and 1/2 cup boiling water in a small bowl; cover and let stand 15 minutes. Drain mushrooms in a colander over a bowl, reserving solids and liquid. Strain reserved liquid through a fine sieve over a small saucepan; bring liquid to a boil. Cook until reduced to 1 tablespoon (about 5 minutes); cool completely. Finely chop mushrooms. Stir reduced liquid and mushrooms into mayonnaise mixture. Cover and chill at least 4 hours.