With LHC commissioned in just a few month ahead, all sorts of ideas about physics beyond the standard model are being explored intensively. A strong-coupling chiral theory appearing at TeV scale remains a possibility but also a very hard scenario to study. When it comes to strongly coupled theories, lattice regularization is by far the most reliable method. But defining exact chiral gauge theory on the lattice remains a difficult problem on its own. We show that the idea to use additional non-gauge, high-scale mirror-sector dynamics to decouple the mirror fermions without breaking the gauge symmetry might lead to a practically manageable solution. We demonstrate, using the exact lattice chirality, that partition functions of lattice gauge theories with vector like fermion representations can be split into \'light\' and \'mirror\' parts, and each contains a chiral representation. Such a splitting is only well defined when both sectors are separately anomaly free. We also prove that, the generating function and therefore the spectrum of an arbitrary chiral gauge theory is a smooth function of the background gauge field, if and only if the anomaly free condition is satisfied. We reached this conclusion by proving some very general properties of an arbitrary chiral gauge theory on lattice, and the results should be of importance for further studies in this field.