Create a container for the lists outside your loop:
int Size = int.Parse(Console.ReadLine());
List<List<string>> listContainer = new List<List<string>>();
for (int i = 0; i < Size; i++)
{
listContainer.Add(new List<string>());
}
You can access them via the index of the container object. For example listContainer[0] would be the first list<string> in the container.
Here is an example of accessing one of the lists and then accessing a value from said list:
int Size = int.Parse(Console.ReadLine());
List<List<string>> listContainer = new List<List<string>>();
for (int i = 0; i < Size; i++)
{
listContainer.Add(new List<string>());
}
listContainer[0].Add("Hi");
Console.WriteLine(listContainer[0][0]);