  Let $\ca$ be a small dg category over a field $k$ and let $\cu$ be a small
full subcategory of the derived category $\cd\ca$ which generate all free dg
$\ca$-modules. Let $(\cb,X)$ be a standard lift of $\cu$. We show that there is
a recollement such that its middle term is $\cd\cb$, its right term is
$\cd\ca$, and the three functors on its right side are constructed from $X$.
This applies to the pair $(A,T)$, where $A$ is a $k$-algebra and $T$ is a good
$n$-tilting module, and we obtain a result of Bazzoni--Mantese--Tonolo. This
also applies to the pair $(\ca,\cu)$, where $\ca$ is an augmented dg category
and $\cu$ is the category of `simple' modules, e.g. $\ca$ is a
finite-dimensional algebra or the Kontsevich--Soibelman $A_\infty$-category
associated to a quiver with potential.
