There's a nice proof by Margulis showing that arithmetic subgroups are indeed lattices using the famous Dani-Margulis non-divergence theorem.
Actually if you will investigate Ratner's original formulations of her theorems, she usually only assumes that $\Gamma$ is discrete, and then concludes something about it having finite-volume.

Furstenberg's proof of Borel's density theorem also come into mind.

Sort of related to dynamics - Kazhdan's property T (i.e. very strong mixing statement) was developed by Kazhdan (and Margulis) to answer Selberg's conjectures about the abelinzation of a lattice.

A more recent development, using the quantitative equidistribution of semisimple periods (proved by Einsiedler-Margulis-Venkatesh), the authors (with the addition of Mohammadi) managed to show ''transport of spectral gap'' of products allowing one to derive a new proof of property tau (for most types of groups, definitely the weird ones included).

Another example can be seen in the proof of Einsiedler-Lindenstrauss-Michel-Venkatesh of Duke's (Linnik-Skubenko) theorem. The statement there is about the $\Gamma$-action on $G/A$ and then they use duality to transfer it to problem about $A$-action over $\Gamma \backslash G$. [There's also a whole industry of counting problems and Diophantine approximation problems related to lattice actions a-la Duke-Sarnak, see the recent book by Gorodnik-Nevo.]

I believe the question is exactly what you call ''Homogeneous dynamics''. I guess the subject's founding fathers, back in Jerusalem, will say it is a mix of ergodic theory, representation theory (and so harmonic analysis), Lie and algebraic group theory with some inputs from geometric group theory and number theory (both analytic, geometry of numbers and algebraic nt), rather than just focusing on the ergodic theory of the matters. So I guess the question is what you are willing to assume and what are you after exactly. If you just want direct corollaries of the pointwise ergodic theorem, then it is a whole different story.