  We show that the coadmissibility of the Iwasawa cohomology of an $L$-analytic
Lubin-Tate $(\varphi_L,\Gamma_L)$-module $M$ is necessary and sufficient for
the existence of a comparison isomorphism between the former and the analytic
cohomology of its Lubin-Tate deformation, which, roughly speaking, is given by
the base change of $M$ to the algebra of $L$-analytic distributions. We verify
that coadmissibility is satisfied in the trianguline case and show that it can
be ``propagated'' to a reasonably large class of modules, provided it can be
proven in the \'etale case.
