In conventional s-wave superconductors, only magnetic impurities exhibit impurity bound states, whereas for an s+- order parameter they can occur for both magnetic and non-magnetic impurities. Impurity bound states in superconductors can thus provide important insight into the order parameter. Here, we present a combined experimental and theoretical study of native and engineered iron-site defects in LiFeAs. Detailed comparison of tunneling spectra measured on impurities with spin fluctuation theory reveals a continuous evolution from negligible impurity bound state features for weaker scattering potential to clearly detectable states for somewhat stronger scattering potentials. All bound states for these intermediate strength potentials are pinned at or close to the gap edge of the smaller gap, a phenomenon that we explain and ascribe to multi-orbital physics.