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We present beta -detected NMR measurements of the spin-lattice relaxation of super(8)Li super(+) implanted into an epitaxial heterostructure based on a 100 nm thick film of ferromagnetic (FM) EuO as a function of temperature through its FM transition. In the FM state, the spin-lattice relaxation rate follows the same temperature dependence, determined by magnon scattering mechanisms, observed in the bulk by super(153)Eu NMR, but above 40 K, the signal is wiped out. We also find that super(8)Li super(+) stopped in material adjacent to the magnetic layer exhibits spin relaxation related to the critical slowing of the Eu spins. A particularly strong relaxation in the Au overlayer suggests an unusual strong nonlocal coupling mechanism to super(8)Li in the metal.