Cohomological spectral-sequence conjecture for locally analytic vectors

Let $G$ be a compact $p$-adic Lie group, let $M$ be a $G$-module in the setting of the paper, and let $\mathrm{R}_{\mathrm{la}}^j(M)$ denote the $j$th derived functor of locally analytic vectors. Spectral-sequence conjecture. There exists a spectral sequence

$$E_2^{i,j}=\mathrm{H}^i\bigl(G,\mathrm{R}_{\mathrm{la}}^j(M)\bigr)\Rightarrow \mathrm{H}^{i+j}(G,M).$$

This would relate group cohomology of the derived locally analytic-vector functors to the cohomology of $M$ and is presented as an analogy with a result cited in the paper.