Yes. As part of the screening process, LOLIN does reject some applications for various reasons.
Please keep in mind that LOLIN takes into consideration the special needs of the rescue dogs when finding homes for them.
Rejected applicants receive a rejection letter. LOLIN is not passing judgment on your family, but is focused on meeting the special needs of the rescued Labs that may have already been displaced multiple times.
LOLIN volunteers do their best in evaluating your application based on the information provided. If you want to provide additional information that may better clarify an issue or additional references on your behalf, you would be free to do so.