Measurements of \( b\to {c\tau}^{-}{\overline{\nu}}_{\tau } \) transitions at colliders are highly motivated for testing lepton flavor universality (LFU), a cornerstone hypothesis of the Standard Model (SM). Potential observations of LFU violation could provide significant evidence for physics beyond the SM (BSM). The substantial production of b-hadrons at the Electron-Ion Collider (EIC) would highlight its potential to support LFU testing and complement studies conducted at other experimental facilities. In this paper, we study the production of b-hadrons in deep inelastic scattering processes at the EIC with \( \sqrt{s} \) = 100 GeV. We estimate the b-hadron yields at the EIC to reach \( \mathcal{O}\left({10}^9\right) \) with an integrated luminosity of up to 103 fb−1. Furthermore, we perform a systematic study on various b-hadron decays, exploring the sensitivities of LFU-violating observables, including RJ/ψ, \( {R}_{D_s^{\left(\ast \right)}} \) and \( {R}_{\Lambda_c} \) . Detailed strategies for track-based event reconstruction are investigated for these observables. We also include a discussion of the annihilation process \( {B}_c^{+}\to {\tau}^{+}{\nu}_{\tau } \) . Finally, we provide a theoretical interpretation of the projected sensitivities within the framework of low energy effective field theory (LEFT). Our analysis indicates that the EIC has the potential to constrain the relevant Wilson coefficients at \( \mathcal{O}(0.1) \) , offering complementary insights to other measurements.
