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 Åbreaks 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 (Mstar ≃ 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.