S.B.
Your son is grieving -- and you have to go through grief. You can't ignore it and you can't go around it. You have to go through it. Let him know that it is okay to grieve, but that it will get better over time. Expect the cycles of grief: denial, anger, etc. Perhaps you can do some of the things people do for comfort when they are grieving the loss of a human loved one. If it will help, maybe you can have a memorial ceremony where you talk about good memories and fun traits your dog had. Then have a prayer, thanking God for giving such a good companion to you for so long. Then, after the tears, go out to eat or have something special for dinner. Perhaps you and your son can put together a scrapbook and/or a memory box about Lilah. Maybe you can take a donation of dog food and treats to your local animal shelter or animal rescue. These are time-proven ways of helping people come to terms with grief. Maybe one of them will help your son.
And my condolences!
S. B.