We characterize Feshbach resonances in all isotopologs of the $\mathrm{Li}-\mathrm{Li}$ system with improved interaction potentials. Starting from spectroscopically accurate Morse/long-range (MLR) potential-energy curves for the singlet ($X{}^1\mathrm{\Sigma }^{+}$) and triplet ($a{}^3\mathrm{\Sigma }^{+}$) electronic states of ${\mathrm{Li}}_2$, we apply small phenomenological inner-wall adjustments [following Julienne and Hutson, Phys. Rev. A 89, 052715 (2014)] and fit the resulting potentials to threshold measurements for the ${}^6\mathrm{Li}-{}^6\mathrm{Li}$ and ${}^7\mathrm{Li}-{}^7\mathrm{Li}$ isotopologs, including binding energies, scattering lengths, and Feshbach resonance positions. Using the optimized potentials in coupled-channel scattering calculations, we predict and characterize $s$-wave Feshbach resonances in the ${}^6\mathrm{Li}-{}^7\mathrm{Li}$ isotopolog. In its lowest-energy hyperfine channel, all resonances are narrow ($\sim 0.01-0.1\mathrm{G}$), strongly closed-channel dominated, and predominantly triplet in electronic spin character, in marked contrast to the homonuclear systems. These results provide a foundation for designing Raman optical-transfer pathways to produce ultracold ${\mathrm{Li}}_2$ molecules in deeply bound rovibrational levels of both the $X{}^1\mathrm{\Sigma }^{+}$ and $a{}^3\mathrm{\Sigma }^{+}$ potentials across all three isotopologs.

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• Atomic & molecular processes in external fields
• Cold and ultracold molecules
• Fine & hyperfine structure
• Interatomic & molecular potentials
• Isotope shift
• Long-range interactions
• Molecular dissociation
• Potential energy surfaces
• Scattering theory
• Ultracold collisions
• van der Waals interaction
• Feshbach resonance