Supernova (SN) H0pe was discovered as a new transient in James Webb Space Telescope (JWST) NIRCam images of the galaxy cluster PLCK G165.7+67.0 taken as part of the Prime Extragalactic Areas for Reionization and Lensing Science (PEARLS) JWST GTO program (ID 1176) on 2023 March 30. The transient is a compact source associated with a background galaxy that is stretched and triply imaged by the strong gravitational lensing of the cluster. This paper reports spectra in the 950–1370 nm observer frame of two of the galaxy images obtained with Large Binocular Telescope (LBT) Utility Camera in the Infrared (LUCI) in long-slit mode two weeks after the JWST observations. The individual and average spectra show the [O II] λλ3727,3730 doublet and the Balmer and 4000 Å breaks at redshift z = 1.783 ± 0.002. The code investigating galaxy emission (CIGALE) best-fit model of the spectral energy distribution indicates that the host galaxy of SN H0pe is massive (M_star ≃ 6 × 10¹⁰ M_⊙ after correcting for a magnification factor μ ∼ 7) with a predominantly intermediate-age (∼2 Gyr) stellar population, moderate extinction, and a magnification-corrected star formation rate ≃13 M_⊙ yr⁻¹, consistent with being below the main sequence of star formation. These properties suggest that H0pe might be a type Ia SN. Additional observations of SN H0pe and its host recently carried out with JWST (JWST-DD-4446; PI: B. Frye) will be able to both determine the SN classification and confirm its association with the galaxy analyzed in this work.