Is it always true that the vapor above a mixture of two liquids that don't obey Raoult's law is richer in the more volatile liquid?

No, it is not always true that the vapor above a mixture of two liquids that don't obey Raoult's law is richer in the more volatile liquid. In mixtures that do not obey Raoult's law, the composition of the vapor phase can be more complex and may not necessarily be richer in the more volatile component. The vapor composition will depend on the specific interactions between the components in the mixture and their respective vapor pressures.

No.

The more volatile liquid has a higher vapor pressure than the less volatile one. Therefore, the vapor pressure of the more volatile liquid over the mixture will be higher than that of the less volatile one. However, the vapor will not necessarily be richer in the more volatile liquid. The composition of the vapor will depend on the relative vapor pressures of the two liquids and on the temperature.