Map of monads and left adjoints

Question

Let $(T,\eta,\mu)$, $(T',\eta',\mu')$ be two monads on a category $X$. Let $\theta:T\Rightarrow T'$ be a map of monads. Then, we have an induced functor $X^\theta:X^{T'}\rightarrow X^T$ (from the $T'$-algebras to the $T$-algebras).
Any example of a $X^\theta$ functor that doesn't have a left adjoint?