<p>The Lawson, Scott, and Alexandroff topologies are three of the most important topological structures in domain theory. On the classical real line, all these topologies are (quasi-)metrizable. However, it is quite surprising that little attention has been paid to exploring the relationships between fuzzy metrics and these topologies on the fuzzy real line. In this paper, we investigate the metrization properties of the Lawson, Alexandroff, and Scott topologies in the context of the fuzzy real line. We show that both the Alexandroff and Lawson topologies are <i>L</i>-quasi-metrizable in the sense of Erceg, whereas the Scott topology is pointwise <i>L</i>-quasi-metrizable in the sense of Shi. Furthermore, we demonstrate that the space of fuzzy interval numbers is homeomorphic to a subspace of the product of two fuzzy number spaces. These findings reveal a harmonious interaction between fuzzy quasi-metrics and the three foundational topologies on the fuzzy real line, thereby reinforcing the theoretical soundness and applicability of both Erceg’s and Shi’s frameworks of <i>L</i>-quasi-metrics.</p>