The Legendrian contact homology dga can in certain situation be endowed with a relative Calabi-Yau structure. We discuss the proof and  geometric consequences for the augmentation variety, e.g. the property of being a holomorphic Lagrangian in favourable situations. Even in cases when there is no relative Calabi-Yau structure, e.g. for the knot contact homology dga of Ekholm-Etynre-Ng-Sullivan, we use similar techniques show that the the holomorphic Lagrangian property still holds for the augmentation variety. This is joint work with N. Legout.