  Low-temperature electron paramagnetic resonance measurements are performed on
single crystals of LiY_{1-x}Gd_xF_4 with weak x=0.005 and moderate x=0.05
concentration of Gd ions. Modeling of the experimental spectra allows us to
precisely determine microscopic parameters of the spin Hamiltonian of the
parent LiGdF4 material, including the nearest-neighbor exchange constant. The
obtained parameters are further tested by comparing a strongly anisotropic
Curie-Weiss temperature obtained for LiGdF4 in our static magnetization
measurements with theoretically computed values. We find a fine balance between
principal magnetic interactions in LiGdF4, which results in a hidden magnetic
frustration presumably leading to a delayed magnetic ordering and an enhanced
magnetocaloric effect at low temperatures.
