You don't need a Lookup, a simple GroupBy would do:
var mostCommon = MyCollection
.GroupBy(r => r)
.Select(grp => new { Value = grp.Key, Count = grp.Count() })
.OrderByDescending(x => x.Count)
.First()
Console.WriteLine(
"Value {0} is most common with {1} occurrences",
mostCommon.Value, mostCommon.Count);