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We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that $E$ is a quasi-Baire space iff $(E,T\left(𝒰\right),T\left({𝒰}^{-1}\right))$, is a pairwise Baire bitopological space, where $𝒰$, is a quasi-uniformity that determines, in $L$. Nachbin’s sense, the topological ordered space $E$.