Multimode spectro-temporal non-Gaussian quantum states of light play a crucial role in continuous-variable quantum information processing. In particular, the non-Gaussian quantum states generated through a single-photon addition (SPA) to multimode quantum fields at telecommunication wavelengths constitute a useful resource for quantum technologies. We present a detailed theoretical analysis and numerical simulations of single-photon addition (SPA) and mode-selective single-photon addition (MSSPA) to a multimode quantum field at telecommunication wavelengths. The analysis is performed for congruently grown lithium niobate (LN), 5% MgO-doped lithium niobate (MgO:LN) and various concentrations of ZnO-doped lithium niobate (ZnO:LN) bulk crystals. We investigate MSSPA using type-II parametric down-conversion (PDC) and SPA using the type-I PDC processes. We further present spectro-temporal mode-selective SPA at the telecom wavelength using 5% MgO:LN for temperatures ranging from 0^∘ C to 15^∘ C. In addition, we perform simulations to investigate SPA based on the noncollinear type-I PDC configuration. These theoretical results identify optimal experimental conditions and phase-matching parameters to achieve SPA and mode-selective SPA for LN-based crystals, providing a potential platform for non-Gaussian quantum state engineering at telecommunication wavelengths, mainly at 1550 nm.