Centrally located diffuse radio emission has been observed in both merging and non-merging galaxy clusters. Depending on their morphology and size, we distinguish between giant radio haloes, which occur predominantly in merging clusters, and mini haloes, which are found in non-merging, cool-core clusters. In recent years, cluster-scale radio emission has also been observed in clusters with no sign of major mergers, showing that our knowledge of the mechanisms that lead to particle acceleration in the intra-cluster medium (ICM) is still incomplete. Low-frequency sensitive observations are required to assess whether the emission discovered in these few cases is common in galaxy clusters or not. With this aim, we carried out a campaign of observations with the LOw Frequency ARay (LOFAR) in the frequency range 120–168 MHz of nine massive clusters selected from the Planck SZ catalogue, which had no sign of major mergers. In this paper, we discuss the results of the observations that have led to the largest cluster sample studied within the LOFAR Two-metre Sky Survey, and we present Chandra X-ray data used to investigate the dynamical state of the clusters, verifying that the clusters are currently not undergoing major mergers, and to search for traces of minor or off-axis mergers. We discover large-scale steep-spectrum emission around mini haloes in the cool-core clusters PSZ1G139.61+24 and RXJ1720.1+2638, which is not observed around the mini halo in the non-cool-core cluster A1413. We also discover a new 570 kpc-halo in the non-cool-core cluster RXCJ0142.0+2131. We derived new upper limits to the radio power for clusters in which no diffuse radio emission was found, and we discuss the implication of our results to constrain the cosmic-ray energy budget in the ICM. We conclude that radio emission in non-merging massive clusters is not common at the sensitivity level reached by our observations and that no clear connection with the cluster dynamical state is observed. Our results might indicate that the sloshing of a dense cool core could trigger particle acceleration on larger scales and generate steep-spectrum radio emission.