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The microscopic details of the suppression of antiferromagnetic order in the Kondo-lattice series Ce$_{1-x}$La$_{x}$Cu$_{2}$Ge$_{2}$ due to nonmagnetic dilution by La are revealed through neutron diffraction results for $x=0.20$, $0.40$, $0.75$, and $0.85$. Magnetic Bragg peaks are found for $0.20\le x\le0.75$, and both the N\'{e}el temperature, $T_{\textrm{N}}$, and the ordered magnetic moment per Ce, $\mu$, linearly decrease with increasing $x$. The reduction in $\mu$ points to strong hybridization of the increasingly diluted Ce $4f$ electrons, and we find a remarkable quadratic dependence of $\mu$ on the Kondo-coherence temperature. We discuss our results in terms of local-moment- versus itinerant-type magnetism and mean-field theory, and show that Ce$_{1-x}$La$_{x}$Cu$_{2}$Ge$_{2}$ provides an exceptional opportunity to quantitatively study competing magnetic interactions in a Kondo lattice., Comment: Supplementary material included