Catalysis of the reaction: 2-oxoglutarate + N(6),N(6),N(6)-trimethyl-L-lysine + O2 = 3-hydroxy-N(6),N(6),N(6)-trimethyl-L-lysine + CO2 + succinate.
N6,N6,N6-trimethyl-L-lysine,2-oxoglutarate:oxygen oxidoreductase (3-hydroxylating)