Looping over ILookup, accessing values

Each entry in ILookup is another IEnumerable

foreach (var item in lookupTable)
{
    Console.WriteLine(item.Key);
    foreach (var obj in item)
    {
        Console.WriteLine(obj);
    }
}

EDIT

A simple example:

var list = new[] { 1, 2, 3, 1, 2, 3 };
var lookupTable = list.ToLookup(x => x);
var orgArray  = lookupTable.SelectMany(x => x).ToArray();

ILookup is a list of lists:

public interface ILookup<TKey, TElement> : IEnumerable<IGrouping<TKey, TElement>>

So because IGrouping<TKey, TElement> is (implements)...

IEnumerable<TElement>

...a lookup is

IEnumerable<IEnumerable<TElement>>

In your case TElement is also a list, so you end up with

IEnumerable<IEnumerable<List<CustomObject>>>

So this is how you can loop through the customers:

foreach(IGrouping<string, List<CustomObject>> groupItem in lookupTable)
{
    groupItem.Key;
    // groupItem is <IEnumerable<List<CustomObject>>
    var customers = groupItem.SelectMany(item => item);
}

I create an enumeration using the keys first, which I find easier to follow.

IEnumerable<string> keys = lookupTable.Select(t => t.Key);
foreach(string key in keys)
{
    // use the value of key to access the IEnumerable<List<CustomObject>> from the ILookup
    foreach( List<CustomObject> customList in lookupTable[key] )
    {
        Console.WriteLine(customList);
    }        
}