For a Riemannian manifold
(
M
,
g
)
(M,g)
with strictly convex boundary
∂
M
\partial M
, the lens data consist of the set of lengths of geodesics
γ
\gamma
with end points on
∂
M
\partial M
, together with their end points
(
x
−
,
x
+
)
∈
∂
M
×
∂
M
(x_-,x_+)\in \partial M\times \partial M
and tangent exit vectors
(
v
−
,
v
+
)
∈
T
x
−
M
×
T
x
+
M
(v_-,v_+)\in T_{x_-} M\times T_{x_+} M
. We show deformation lens rigidity for such manifolds with a hyperbolic trapped set and no conjugate points. This class contains all manifolds with negative curvature and strictly convex boundary, including those with non-trivial topology and trapped geodesics. For the same class of manifolds in dimension
2
2
, we prove that the set of end points and exit vectors of geodesics (i.e., the scattering data) determines the Riemann surface up to conformal diffeomorphism.