  An understanding of the relationship between radio-loud active galaxies and
their large-scale environments is essential for realistic modelling of
radio-galaxy evolution and environmental impact, for understanding AGN
triggering and life cycles, and for calibrating galaxy feedback in cosmological
models. We use the LOFAR Two-Metre Sky Survey (LoTSS) Data Release 1 catalogues
to investigate this relationship. We cross-matched 8,745 radio-loud AGN with
0.08<z<0.4, selected from LoTSS, with two Sloan Digital Sky Survey cluster
catalogues, and find that only 10 percent of LoTSS AGN in this redshift range
have an association, so that the majority of low-redshift AGN (including a
substantial fraction of the most radio-luminous objects) must inhabit haloes
with M < 10^14 M_sun. We find that the probability of a cluster association,
and the richness of the associated cluster, is correlated with AGN radio
luminosity, and for the cluster population, the number of associated AGN and
the radio luminosity of the brightest associated AGN is richness-dependent. We
demonstrate that these relations are not driven solely by host-galaxy stellar
mass, supporting models in which large-scale environment is influential in
driving AGN jet activity. At the lowest radio luminosities we find that the
minority of objects with a cluster association are located at larger mean
cluster-centre distances than more luminous AGN, which appears to be driven
primarily by host-galaxy mass. Finally, we also find that FRI radio galaxies
inhabit systematically richer environments than FRIIs. The work presented here
demonstrates the potential of LoTSS for AGN environmental studies. In future,
the full northern-sky LoTSS catalogue, together with the use of deeper
optical/IR imaging data and spectroscopic follow-up with WEAVE-LOFAR, will
provide opportunities to extend this type of work to much larger samples and
higher redshifts.
