CCA2-secure encryption based on LWE/Ring-LWE As I understand it, cryptosystems based on LWE/Ring-LWE are typically only IND-CPA, and fail to satisfy IND-CCA2.  In fact, it appears that chosen ciphertext attacks could allow secret key recovery (!).

What is the best known IND-CCA2 secure encryption algorithm based on (Ring-)LWE?  What about key exchange?
If you don't mind relying on random oracles, the simplest approach is to apply a generic transformation such as Fujisaki-Okamoto to the (Ring-)LWE based scheme you start from. See for example Peikert's PQCrypto'14 paper for a concrete instantiation, and the TCC 2016 paper of Targhi and Unruh for a proof of security of this type of transform in the quantum random oracle model.

Lattice-based CCA2-secure encryption in the standard model is usually obtained using lattice trapdoors. The state-of-the-art construction is due to Micciancio and Peikert (section 6.3 of this EUROCRYPT 2012 paper).