The morphology of quiescent galaxies has been found to be correlated with the activity of their central super massive black hole. In this work, we use data from the first data release of the LOFAR Two-Metre Sky Survey (LoTSS DR1) and the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) to select more than 15 000 quiescent galaxies at z < 0.3 to investigate the connection between radio-loud active galactic nuclei (RLAGNs) and the morphology of their host galaxy. Taking advantage of the depth of LoTSS, we find that the fraction of RLAGNs with L_{150 MHz} > 10²¹ W Hz⁻¹ at fixed stellar mass, velocity dispersion, or surface mass density does not depend on the galaxy projected axis ratio (q). However, the high-power (L_{150 MHz} > 10²³ W Hz⁻¹) RLAGNs are more likely to be found in massive, round galaxies, while the low- and intermediate-power (L_{150 MHz} ≤ 10²³ W Hz⁻¹) RLAGNs have similar distributions of q to non-RLAGN galaxies. We argue that our results support the picture that high-power RLAGNs are more easily triggered in galaxies with a merger-rich history, while low-power RLAGNs can be triggered in galaxies growing mainly via secular processes. Our work also supports the idea that the low-luminosity RLAGN may be sufficient for maintenance-mode feedback in low-mass quiescent galaxies with disc-like morphology, which is based on a simple extrapolation from the observed energy balance between cooling and RLAGN-induced cavities in massive clusters. We find no significant difference between the q distributions of RLAGNs likely to be found in clusters and those likely not found in clusters after controlling the radio luminosity and stellar mass of the two samples, indicating that the environment does not significantly influence the morphology–RLAGN correlation.