  In this work, we try to construct the Lax connections of $T\bar{T}$-deformed
integrable field theories in two different ways. With reasonable assumptions,
we make ansatz and find the Lax pairs in the $T\bar{T}$-deformed affine Toda
theories and the principal chiral model by solving the Lax equations directly.
This way is straightforward but maybe hard to apply for general models. We then
make use of the dynamical coordinate transformation to read the Lax connection
in the deformed theory from the undeformed one. We find that once the inverse
of the transformation is available, the Lax connection can be read easily. We
show the construction explicitly for a few classes of scalar models, and find
consistency with the ones in the first way.
