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International audienceA Lam\'e connection is a logarithmic $\mathrm{sl}(2,\mathbb C)$-connection $(E,\nabla)$ over an elliptic curve $X:\{y^2=x(x-1)(x-t)\}$, $t\not=0,1$, having a single pole at infinity. When this connection is irreducible, we show thatit is invariant by the standard involution andcan be pushed down as a logarithmic $\mathrm{sl}(2,\mathbb C)$-connection over $\mathbb P^1$with poles at $0$, $1$, $t$ and $\infty$.Therefore, the isomonodromic deformation $(E_t,\nabla_t)$of an irreducible Lam\'e connection, when the ellipticcurve $X_t$ vary in the Legendre family, is parametrizedby a solution $q(t)$ of the Painlev\'e VI differential equation $P_{VI}$. We computethe variation of the underlying vector bundle $E_t$ alongthe deformation via Tu moduli map: it is given by another solution$\tilde q(t)$ of $P_{VI}$ equation related to $q(t)$ by the Okamoto symetry $s_2 s_1 s_2$ (Noumi-Yamada notation). Motivated by the Riemann-Hilbert problem for the classicalLam\'e equation, the question whether Painlev\'e transcendents do have poles is raised

Isomonodromic deformation of Lamé connections, Painlevé VI equation and Okamoto symmetry