Alpha-ketoglutarate-dependent dioxygenase that in vitro catalyzes the regio- and stereoselective hydroxylation of L-lysine, leading to (4R)-4-hydroxy-L-lysine. To a lesser extent, can also use (3S)-3-hydroxy-L-lysine as substrate, producing the dihydroxylated product (3R,4R)-3,4-hydroxy-L-lysine. Cannot use D-lysine or L-ornithine as substrate. 2-oxoglutarate + L-lysine + O2 = (4R)-4-hydroxy-L-lysine + CO2 + succinate Binds 1 Fe(2+) ion per subunit. Being totally regio- and stereoselective, this enzyme is of interest for biocatalytic purposes to produce chiral scaffolds that are of synthetic value in the preparation of more complex functionalized chiral molecules such as natural products and analogs. Belongs to the clavaminate synthase family.