  A strong generalized topological space is an ordered pair $\mathbf{X}=\langle
X, \mathcal{T}\rangle$ such that $X$ is a set and $\mathcal{T}$ is a collection
of subsets of $X$ such that $\emptyset, X\in \mathcal{T}$ and $\mathcal{T}$ is
stable under arbitrary unions. A necessary and sufficient condition for a
strong generalized topological space $\mathbf{X}$ to satisfy Urysohn's lemma or
its appropriate variant is shown in $\mathbf{ZF}$. Notions of a U-normal and an
effectively normal generalized topological space are introduced. It is observed
that, in $\mathbf{ZF}+\mathbf{DC}$, every U-normal generalized topological
space satisfies Urysohn's lemma. It is shown that every effectively normal
generalized topological space satisfies Csasz\'ar's modification of Urysohn's
Lemma. A $\mathbf{ZF}$- example of a strong generalized topological normal
space which satisfies the Tietze-Urysohn Extension Theorem and fails to satisfy
Urysohn's Lemma is shown.
