  In this note we reveal a connection between the phase space of lambda models
on $S^{1}\times \mathbb{R}$ and the phase space of double Chern-Simons theories
on $D\times \mathbb{R}$ and explain in the process the origin of the
non-ultralocality of the Maillet bracket, which emerges as a boundary algebra.
In particular, this means that the (classical) $AdS_{5}\times S^{5}$ lambda
model can be understood as a double Chern-Simons theory defined on the Lie
superalgebra $\mathfrak{psu}(2,2|4)$ after a proper dependence of the spectral
parameter is introduced. This offers a possibility for avoiding the use of the
problematic non-ultralocal Poisson algebras that preclude the introduction of
lattice regularizations and the application of the QISM to string sigma models.
The utility of the equivalence at the quantum level is, however, still to be
explored.
