Pass string array in list constructor.
List<string> yourList = new List<string>(strArray);
The reason your first line didn't work was because you are not using the correct syntax. So instead of
List<string> lstArray = strArray.toList<string>;
Use
List<string> lstArray = strArray.ToList<string>();
or
List<string> lstArray = strArray.ToList(); // with less keystrokes, since the array is of type string.
For the 2nd option where you are trying to use Array.CopyTo, it works with array types, not generic list. You are probably getting the error.
The best overloaded method match for
'System.Array.CopyTo(System.Array, int)' has some invalid arguments
Since it expects an array and you are passing a generic list.