  This is the second paper in a series of three papers aiming to study
cohomology of group theoretic Dehn fillings. In the present paper, we derive a
spectral sequence for Cohen-Lyndon triples which can be thought of as a refined
version of the classical Lyndon-Hochschild-Serre spectral sequence in the
settings of group theoretic Dehn fillings. In the next paper arXiv:1908.01290,
we will apply this spectral sequence to study cohomological finiteness
properties of Dehn fillings of acylindrically hyperbolic groups.
