First of all, I'm so very sorry to hear of your loss, I too will be a wreck when that time comes... Not sure if you belonged to a church of any kind, they may be able to point you in a direction? I would imagine the VA would be somewhere to start. I have never dealt with a funeral home, but I would imagine they have plans for this, maybe payments? Cremation is cheaper than full on burial...I bet they have a system in place, a lot more people are low on money than well off, not the first time they have heard this. There is an organization called the wounded warrior project...while I think they help with disabled vets, they may be of some help navigating the VA?
Your dad sounded like a really cool guy, the lion story was great! Please accept my condolences for his passing, take one step at a time, breathe, and things will fall into place. The probate lawyer sounds like a good idea if you can find a way. (edited)