  We investigate the low-temperature behavior of Kondo lattices upon random
depletion of the local $f$-moments, by using strong-coupling arguments and
solving SU($N$) saddle-point equations on large lattices. For a large range of
intermediate doping levels, between the coherent Fermi liquid of the dense
lattice and the single-impurity Fermi liquid of the dilute limit, we find
strongly inhomogeneous states that exhibit distinct non-Fermi liquid
characteristics. In particular, the interplay of dopant disorder and strong
interactions leads to rare weakly screened moments which dominate the bulk
susceptibility. Our results are relevant to compounds like Ce_{x}La_{1-x}CoIn_5
and Ce_{x}La_{1-x}Pb_3
