Not very efficient but very easy to understand approach might be to solve this task recursively. Consider a method which computes permutations for N lists. If you have such a method then you can easily compute permutations for N+1 lists by combining all permutation of N lists with every number in the last list. You should also handle corner case which permutations of 0 lists. Then implementation seems to be straightforward:
IEnumerable> GetAllPermutations(IEnumerable> inputLists)
{
if (!inputLists.Any()) return new [] { Enumerable.Empty() };
else
{
foreach (var perm in GetAllPermutations(inputLists.Skip(1)))
foreach (var x in inputLists.First())
yield return new[]{x}.Concat(perm);
}
}