  The relative positions of the high and low surface brightness regions of
radio-loud active galaxies in the 3CR sample were found by Fanaroff and Riley
to be correlated with their luminosity. We revisit this canonical relationship
with a sample of 5805 extended radio-loud AGN from the LOFAR Two-Metre Sky
Survey (LoTSS), compiling the most complete dataset of radio-galaxy
morphological information obtained to date. We demonstrate that, for this
sample, radio luminosity does *not* reliably predict whether a source is
edge-brightened (FRII) or centre-brightened (FRI). We highlight a large
population of low-luminosity FRIIs, extending three orders of magnitude below
the traditional FR break, and demonstrate that their host galaxies are on
average systematically fainter than those of high-luminosity FRIIs and of FRIs
matched in luminosity. This result supports the jet power/environment paradigm
for the FR break: low-power jets may remain undisrupted and form hotspots in
lower mass hosts. We also find substantial populations that appear physically
distinct from the traditional FR classes, including candidate restarting
sources and ``hybrids''. We identify 459 bent-tailed sources, which we find to
have a significantly higher SDSS cluster association fraction (at $z<0.4$) than
the general radio-galaxy population, similar to the results of previous work.
The complexity of the LoTSS faint, extended radio sources demonstrates the need
for caution in the automated classification and interpretation of extended
sources in modern radio surveys, but also reveals the wealth of morphological
information such surveys will provide and its value for advancing our physical
understanding of radio-loud AGN.
