I think you need something like the following:

SELECT Invoice.Invoice_ID, Invoice.Invoice_Contact, Count(InvoiceLineItems.InvoiceLineItemsID) AS CountOfInvoiceLineItemsID
FROM (Invoice INNER JOIN InvoiceLineItems ON Invoice.Invoice_ID = InvoiceLineItems.InvoiceID) LEFT JOIN InvoicePayments ON Invoice.Invoice_ID = InvoicePayments.InvoiceID
GROUP BY Invoice.Invoice_ID, Invoice.Invoice_Contact, InvoicePayments.InvoicePaymentsID
HAVING (((Count(InvoiceLineItems.InvoiceLineItemsID))>=3) AND ((InvoicePayments.InvoicePaymentsID) Is Null));

The Is Null forces the return of only invoices where there is no payment records beacuse of the outer join.