Catalyzes the hydroxylation of the N(6)-(4-aminobutyl)-L-lysine intermediate produced by deoxyhypusine synthase/DHPS on a critical lysine of the eukaryotic translation initiation factor 5A/eIF-5A. This is the second step of the post-translational modification of that lysine into an unusual amino acid residue named hypusine. Hypusination is unique to mature eIF-5A factor and is essential for its function. [eIF5A protein]-deoxyhypusine + AH2 + O2 = [eIF5A protein]-hypusine + A + H2O Binds 2 Fe(2+) ions per subunit. Protein modification; eIF5A hypusination. Belongs to the deoxyhypusine hydroxylase family.