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The $U_1$ leptoquark is known to be a suitable candidate for explaining thesemileptonic $B$-decay anomalies. We derive precise limits on its parameterspace relevant for the anomalies from the current LHC high-$p_{\rm T}$ dileptondata. We consider an exhaustive list of possible $B$-anomalies-motivated simplescenarios with one or two new couplings that can also be used as templates forobtaining bounds on more complicated scenarios. To obtain precise limits, wesystematically consider all possible $U_1$ production processes that cancontribute to the dilepton searches, including the resonant pair and singleproductions, nonresonant $t$-channel $U_1$ exchange, as well as its largeinterference with the Standard Model background. We demonstrate how theinclusion of resonant production contributions in the dilepton signal can leadto appreciably improved exclusion limits. We point out new search channels of$U_1$ that can act as unique tests of the flavour-motivated models. Thetemplate scenarios can also be used for future $U_1$ searches at the LHC. Wecompare the LHC limits with other relevant flavour bounds and find that aTeV-scale $U_1$ can accommodate both $R_{D^{(*)}}$ and $R_{K^{(*)}}$ anomalieswhile satisfying all the bounds.

Precise limits on the charge-$2/3$ $U_1$ vector leptoquark