A novel linked‐half‐sandwich lutetium–bis(allyl) complex (C5Me4C5H4N)Lu(η3‐C3H5)2 (1) attached by a pyridyl‐functionalized cyclopentadienyl ligand was synthesized and fully characterized. Complex 1 in combination with Ph3CB(C6F5)4 exhibited unprecedented dual catalysis with outstanding activities in highly syndiotactic (rrrr>99 %) styrene polymerization and distinguished cis‐1,4‐selective (99 %) butadiene polymerization, respectively. Strikingly, this catalyst system exhibited remarkable activity (396 kg copolymer (molLu h)−1) for the copolymerization of butadiene and styrene. Irrespective of whether the monomers were fed in concurrent mode or sequential addition of butadiene followed by styrene, diblock copolymers were obtained exclusively, which was confirmed by a kinetics investigation of monomer conversion of copolymerization with time. In the copolymers, the styrene incorporation rate varied from 4.7 to 85.4 mol %, whereas the polybutadiene (PBD) block was highly cis‐1,4‐regulated (95 %) and the polystyrene segment remained purely syndiotactic (rrrr>99 %). Correspondingly, the copolymers exhibited glass transition temperatures (Tg) around −107 °C and melting points (Tm) around 268 °C; typical values for diblock microstructures. Such copolymers cannot be accessed by any other methods known to date. X‐ray powder diffraction analysis of these diblock copolymers showed that the crystallizable syndiotactic polystyrene (syn‐PS) block was in the toluene δ clathrate form. The AFM micrographs of diblock copolymer showed a remarkable phase‐separation morphology of the cis‐1,4‐PBD block and syn‐PS block. This represents the first example of a lutetium‐based catalyst showing both high activity and selectivity for the (co)polymerization of styrene and butadiene. Challenge to a dual: Under the activation of Ph3CB(C6F5)4, a pyridyl‐functionalized cyclopentadienyl lutetium–bis(allyl) complex exhibited unprecedented dual behavior for syndiotactic (rrrr>99 %) styrene polymerization and cis‐1,4‐selective (99 %) butadiene polymerization.