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!
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.