Hello,
Rotate works on graphics primitives (Sphere, Cylinder, Cuboid ...). ListContourPlot3D is not a graphics primitive.
In 3D, Rotate can rotate around any given 3D vector. Check this:
Manipulate[
Show[
Graphics3D@Sphere[],
Graphics3D@Rotate[Cuboid[], angle, {1, 0, 0}],
PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}, {-1.5, 1.5}}
],
{{angle, 0}, -\[Pi], \[Pi]}
]
