A search for new heavy resonances decaying to a pair of Higgs bosons in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. Data were collected by the CMS detector at the LHC from 2016 to 2018, corresponding to an integrated luminosity of 138 $\text{fb}^{-1}$. The search considers resonances with a mass between 0.8 and 4.5 TeV using events in which one Higgs boson decays into a bottom quark-antiquark pair and the other decays into final states with either one or two charged leptons. Specifically, these include the single-lepton final state of the $\mathrm{HH} \rightarrow \mathrm{b\bar{b}WW^*} \rightarrow \mathrm{b\bar{b}}\ell \nu \mathrm{q\bar{q}}$ decay and the dilepton final states of both the $\mathrm{HH} \rightarrow \mathrm{b\bar{b}WW^*} \rightarrow \mathrm{b\bar{b}}\ell \nu \ell \nu$ and $\mathrm{HH} \rightarrow \mathrm{b\bar{b}}\tau \tau \rightarrow \mathrm{b\bar{b}}\ell \nu \nu \ell \nu \nu$ decays, where $\ell$ in the final state corresponds to $e$ or $\mu$. The signal is extracted using a two-dimensional maximum likelihood fit of the $\mathrm{H} \rightarrow \mathrm{b\bar{b}}$ jet mass and $\mathrm{HH}$ invariant mass distributions. No significant excess above the standard model expectation is observed in data. Model-independent exclusion limits are placed on the the product of the cross section and branching fraction ($\sigma \mathcal{B}$) for spin-0 and spin-2 massive bosons decaying to $\mathrm{HH}$. The results are interpreted in the context of radion and bulk graviton production in models with a warped extra spatial dimension.

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