Wanted to post this as a comment as a side note to the accepted answer, but that got a bit unclear. So purely as a side note:
If you have no need for the objects themselves and you want to have your project clear of further unused classes, you can parse with something like:
var list = JObject.Parse(json)["People"].Select(el => new { FirstName = (string)el["FirstName"], LastName = (string)el["LastName"] }).ToList();
var firstNames = list.Select(p => p.FirstName).ToList();
var lastNames = list.Select(p => p.LastName).ToList();
Even when using a strongly typed person class, you can still skip the root object by creating a list with JObject.Parse(json)["People"].ToObject<List<Person>>()
Of course, if you do need to reuse the objects, it's better to create them from the start. Just wanted to point out the alternative ;)