  A search is presented for direct pair production of the stop, the
supersymmetric partner of the top quark, in a decay through an $R$-parity
violating coupling to a charged lepton and a $b$-quark. The dataset corresponds
to an integrated luminosity of 140 fb$^{-1}$ of proton-proton collisions at a
center-of-mass energy of $\sqrt{s}$ = 13 TeV collected between 2015 and 2018 by
the ATLAS detector at the LHC. The final state has two charged leptons
(electrons or muons) and two $b$-jets. The results of the search are
interpreted in the context of a Minimal Supersymmetric Standard Model with an
additional $B-L$ gauge symmetry that is spontaneously broken. No significant
excess is observed over the Standard Model background and exclusion limits on
stop pair production are set at 95% confidence level. The corresponding lower
limits on the stop mass for 100% branching ratios to a $b$-quark and an
electron, muon, or tau-lepton are 1.9 TeV, 1.8 TeV and 800 GeV, respectively,
extending the reach of previous LHC searches.
