This is a continuation of the work where the notions of Lebesgue uniformity and Lebesgue quasi uniformity in a texture space were introduced. It is  well known that the quasi uniform space with a compact topology has the Lebesgue property. This result is extended to direlational quasi uniformities and dual dicovering quasi uniformities. Additionally we discuss the completeness of lebesgue di-uniformities and dual dicovering lebesgue di-uniformities.