Please call the emergency vet right away, even if you don't take him in. I had a dog that did that and she was very ill. By the time I realize it I had to make a quick choice, keep her alive or put her down. I kepted her alive but it cost my dearly.
I would see if you can get him to drink some pedilite water ( clear) this might help, but ask the emergency vet.
Please update when you can. I wish you and your pet well.
Not eating or drinking can be a sign of anything from an upset stomach to toothache to virus. Lethargy could also be related, in those cases, as a side effect of not having any nutrition or even as a symptom of an ache. (When we don't feel well, or we haven't eaten because we don't feel well for some time, we don't have a lot of energy either.) Vomiting is one of those symptoms that can accompany so many conditions, as well. And, if your pet is vomiting without ingesting food, then he/she is losing even more fluids and will dehydrate more rapidly.
If your dog was only not interested in food, then I'd say to just pamper him/her and offer a small-sized bland diet. However, not drinking is more serious because dehydration can lead to organ damage - and, we all know, death.
At this point, if your dog hasn't drank water for 3 days without any obvious reason, you should seek veterinarian help - especially considering the vomiting you mention. Your pet's doctor can do lab work to check for underlying illnesses.
Good luck!