Broadband dielectric spectroscopy (BDS) is used to probe the chain and segmental dynamics of A(2),B-2, and AB(2) miktoarm star copolymers based on polystyrene (PS, A block) and polyisoprene (PI, B block) that display lamellar morphologies as determined using small-angle X-ray scattering (SAXS). While no changes in the distribution of PI segmental relaxation times are observed with variation of the molecular architecture, an unexpected increase in the normalized PI chain relaxation intensity is realized for AB, miktoarm star copolymers as well as a change in the distribution of chain relaxation rates as compared to A(2),B-2, and AB diblock copolymer systems. This result is attributed to asymmetry in the molecular architecture near the junction point, which affects the osmotic constraint of the tethered PI chains within the interfacial region of the lamellae. The results highlight the importance of macromolecular design on fundamental chain dynamics in phase-separated thermoplastic elastomers.