  Using ion-implanted $^8$Li $\beta$-detected NMR, we study the evolution of
the correlated metallic state of LaNiO$_3$ in a series of LaNiO$_3$/LaAlO$_3$
superlattices as a function of bilayer thickness. Spin-lattice relaxation
measurements in an applied field of 6.55 T reveal two equal amplitude
components: one with metallic ($T$-linear) $1/T_{1}$, and a second with a more
complex $T$-dependence. The metallic character of the slow relaxing component
is only weakly affected by the LaNiO$_3$ thickness, while the fast component is
much more sensitive, exhibiting the opposite temperature dependence (increasing
towards low $T$) in the thinnest, most magnetic samples. The origin of this
bipartite relaxation is discussed.
