No: the answer is often negative in the non-discrete case.

For instance, non-compact simple connected Lie group $G$ has no proper normal cocompact subgroup. But it has cocompact lattices, and also has connected cocompact proper subgroups (e.g., upper triangular matrices in $\mathrm{SL}_n(\mathbf{R})$ or $\mathrm{SL}_n(\mathbf{C})$, for $n\ge 2$).