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Leptoquarks with masses between 2 TeV and 50 TeV are commonly invoked toexplain deviations between data and Standard-Model (SM) predictions of severalobservables in the decays $b\to c\tau \bar\nu$ and $b\to s \ell^+\ell^-$ with$\ell=e,\mu$. While Leptoquarks appear in theories unifying quarks and leptons,the corresponding unification scale $M_{QLU}$ is typically many orders ofmagnitude above this mass range. We study the case that the mass gap betweenthe electroweak scale and $M_{QLU}$ is only populated by scalar Leptoquarks andSM particles, restricting ourselves to scenarios addressing the mentionedflavour anomalies, and determine the renormalisation-group evolution ofLeptoquark couplings to fermions below $M_{QLU}$. In the most general case, weconsider three SU(2) triplet Leptoquarks $S_3^\ell$, $\ell=e,\mu,\tau$, whichcouple quark doublets to the lepton doublet $(\nu_\ell,\ell^-)$ to address the$b\to s \ell^+\ell^-$ anomalies. In this case, we find a scenario in which theLeptoquark couplings to electrons and muons are driven to the same infraredfixed point, so that lepton flavour universality emerges dynamically. However,the corresponding fixed point for the couplings to taus is necessarily oppositein sign, leading to a unique signature in $b \to s\tau^+\tau^-$. For $b\toc\tau \bar\nu$ we complement these with either an SU(2) singlet $S_1^\tau$ ordoublet $R_2^\tau$ and study further the cases that also these Leptoquarks comein three replicas. The fixed point solutions for the $S_3^\ell$ couplingsexplain the $b\to s \ell^+\ell^-$ data for $S_3^{e,\mu}$ masses around 10 TeV.$b\to c\tau \bar\nu$ data can only be fully explained by couplings exceedingtheir fixed-point values and evolving into Landau poles at high energies, sothat one can place an upper bound on $M_{QLU}$ between $10^{8}$ and $10^{11}$GeV.

Renormalisation group analysis of scalar Leptoquark couplings addressing flavour anomalies: emergence of lepton-flavour universality