NullReferenceException in a query involving null foreign key - vb.net

Question

NullReferenceException in a query involving null foreign key
I have a VB project making use of an odata service and linq queries. (The previous sentence is full of things I've never done before, so this might get rough.)
There is an "Employees" table and an "Application" table, linked in a 1-to-1 relationship. I'm trying to figure out how to make use of that relationship to join the tables and query one field from each.
This query is the closest I've come (it compiles, unlike some other variations I tried):
Dim Emps = (From e In ctx.Employees Select e.FirstName, e.Application.AppNo)
I can even check how many records are in the result:
Console.WriteLine(Emps.Count)
and get a reasonable number. But any attempt to do anything else with the result causes an exception to be thrown. For eaxmple, I did this:
Console.WriteLine("----")
Console.WriteLine(Emps.FirstOrDefault.FirstName)
Console.WriteLine("====")
and it threw:
Unhandled Exception: System.NullReferenceException: An entry returned by the navigation property 'Application' is null and cannot be initialized. You should check for a null value before accessing this property.
at System.Data.Services.Client.Materialization.ODataEntityMaterializer.CheckEntryToAccessNotNull(MaterializerEntry entry, String name)
at System.Data.Services.Client.Materialization.ODataEntityMaterializer.ProjectionValueForPath(MaterializerEntry entry, Type expectedType, ProjectionPath path)
at System.Data.Services.Client.Materialization.ODataEntityMaterializerInvoker.ProjectionValueForPath(Object materializer, Object entry, Type expectedType, Object path)
at _dynamic_ODataEntityMaterializerInvoker_ProjectionValueForPath(Object , Object , Type , Object )
at lambda_method(Closure , Object , Object , Type )
at System.Data.Services.Client.ProjectionPlan.Run(ODataEntityMaterializer materializer, ODataEntry entry, Type expectedType)
at System.Data.Services.Client.Materialization.ODataEntityMaterializer.ReadImplementation()
at System.Data.Services.Client.MaterializeAtom.MoveNextInternal()
at System.Data.Services.Client.MaterializeAtom.MoveNext()
at System.Linq.Enumerable.<CastIterator>d__1`1.MoveNext()
at System.Linq.Enumerable.FirstOrDefault[TSource](IEnumerable`1 source)
at System.Data.Services.Client.DataServiceQueryProvider.ReturnSingleton[TElement](Expression expression)
at System.Data.Services.Client.DataServiceQueryProvider.Execute[TResult](Expression expression)
at System.Linq.Queryable.FirstOrDefault[TSource](IQueryable`1 source)
at odata.Odata.Main() in H:\Visual Studio 2015\Projects\odata\odata\Odata.vb:line 52
Notice that I got the exception about a null Application even though I was only trying to print the other field, which has nothing to do with Application, which I think is pretty weird. The exception occurred after the "----" was printed but before the "====".
I guess there is a null foreign key in at least one of the records (an Employee without an Application). In that case I'd like to have an empty string or some other placeholder value for e.Application.AppNo but I can't figure out how to tell it to do that.
In more SQL-like syntax, it would be
FROM Employees e
SELECT
e.FirstName,
CASE WHEN e.Application IS NOT NULL
THEN e.Application.AppNo
ELSE ''
END AS AppNo
But all attempts to twist that into a vb/linq statement have resulted in syntax errors.
It's possible I don't understand the schema well enough. I see other questions using explicit join syntax in linq, but I don't know how to do that here, since I don't know what the foreign key field is actually called; all I know is there's something in the odata magic that lets me use e.Application.foo where foo is a field in the Application table and e is an Employees record.
The documentation from the provider of the odata service is of very low quality. (Short code examples in VB, provided as screenshots not text; full dumps of the HTTP requests and responses corresponding to the sample queries, including one XML response over 50 pages long; and on the topic of authentication, a reference to the HTTP Basic "RCF")
UPDATE
The suggestion from Mark generated a new exception:
Unhandled Exception: System.NotSupportedException: Constructing or initializing instances of the type VB$AnonymousType_0`2[System.String,System.Object] with the expression (e.Application != null) is not supported.
at System.Data.Services.Client.ProjectionAnalyzer.NonEntityProjectionAnalyzer.VisitBinary(BinaryExpression b)
at System.Data.Services.Client.ALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.DataServiceALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.ALinqExpressionVisitor.VisitConditional(ConditionalExpression c)
at System.Data.Services.Client.ProjectionAnalyzer.NonEntityProjectionAnalyzer.VisitConditional(ConditionalExpression c)
at System.Data.Services.Client.ALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.DataServiceALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.ALinqExpressionVisitor.VisitExpressionList(ReadOnlyCollection`1 original)
at System.Data.Services.Client.ALinqExpressionVisitor.VisitNew(NewExpression nex)
at System.Data.Services.Client.ProjectionAnalyzer.NonEntityProjectionAnalyzer.VisitNew(NewExpression nex)
at System.Data.Services.Client.ALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.DataServiceALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.ProjectionAnalyzer.NonEntityProjectionAnalyzer.Analyze(Expression e, PathBox pb, DataServiceContext context)
at System.Data.Services.Client.ProjectionAnalyzer.Analyze(LambdaExpression e, PathBox pb, DataServiceContext context)
at System.Data.Services.Client.ProjectionAnalyzer.AnalyzeResourceExpression(LambdaExpression lambda, ResourceExpression resource, DataServiceContext context)
at System.Data.Services.Client.ProjectionAnalyzer.Analyze(LambdaExpression le, ResourceExpression re, Boolean matchMembers, DataServiceContext context)
at System.Data.Services.Client.ResourceBinder.AnalyzeProjection(MethodCallExpression mce, SequenceMethod sequenceMethod, Expression& e)
at System.Data.Services.Client.ResourceBinder.VisitMethodCall(MethodCallExpression mce)
at System.Data.Services.Client.ALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.DataServiceALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.ALinqExpressionVisitor.VisitExpressionList(ReadOnlyCollection`1 original)
at System.Data.Services.Client.ALinqExpressionVisitor.VisitMethodCall(MethodCallExpression m)
at System.Data.Services.Client.ResourceBinder.VisitMethodCall(MethodCallExpression mce)
at System.Data.Services.Client.ALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.DataServiceALinqExpressionVisitor.Visit(Expression exp)
at System.Data.Services.Client.ResourceBinder.Bind(Expression e, DataServiceContext context)
at System.Data.Services.Client.DataServiceQueryProvider.Translate(Expression e)
at System.Data.Services.Client.DataServiceQuery`1.QueryComponents(ClientEdmModel model)
at System.Data.Services.Client.DataServiceRequest.GetQuerySetCount(DataServiceContext context)
at System.Data.Services.Client.DataServiceQueryProvider.ReturnSingleton[TElement](Expression expression)
at System.Data.Services.Client.DataServiceQueryProvider.Execute[TResult](Expression expression)
at System.Linq.Queryable.Count[TSource](IQueryable`1 source)
at odata.Odata.Main() in H:\Visual Studio 2015\Projects\odata\odata\Odata.vb:line 51
This one happens at the attempt to print Emps.Count