A couple of things come to mind about this issue. First, you need to realize that persons in early stage dementia are beginning to lose their reasoning abilities, so that trying to reason with your husband about his behavior might not work, as you have already discovered.   Facts, logic, sarcasm, and lengthy explanations are often lost on a person with impaired memory, so "reminding" him that he's spending unnecessary money isn't very likely to resonate with him.   Even if you should ask him nicely not to do it anymore, and he agrees, his short-term memory is probably on the fritz so that he won't remember it later. As he's losing more of himself to the disease, he wants to hold onto as many familiar things as possible, and for some reason, lottery tickets are one of those things. It seems illogical to you, but this isn't a logical disease.

Trying to convince him to put a stop to the behavior by arguing with him probably isn't the best way to go. People with dementia can get quite defensive when they feel that someone's trying to take away their independence.  A much better use of your time might be to look for some alternatives that don't involve confrontation.  Is it possible to reduce the amount of cash he carries with him, so that he is prevented from spending as much?   Perhaps putting a small amount in an envelope marked "lottery tickets" will help him spend less while still allowing him to "have his way."  Could you try to find someone else who can accompany him on his trips? Giving them a list of other errands to accomplish will occupy their time and perhaps make it easier to overlook a visit to the convenience store.  Distractions at home can also work.  Asking his help with some projects he can work on around the house can alleviate feelings of worthlessness and boredom, and occupy his interest.   You may have to take the initiative to come up with things, such as sorting through tools or a drawer of junk, or shredding old papers, and might have to get him started on it. Sometimes it's effective to just leave a box of familiar things on the dining kitchen table and see if they spark his interest.

The driving issue is another concern. You don't mention when he was diagnosed, or what stage of dementia he is in, but you do say that at some point he'll no longer be able to drive. Have you talked with his doctor about this? Typically, the person with dementia won't realize when the time has come to give up driving, so someone else has to step in. But as unpleasant as it is for most families to face this issue, it is preferable to the risks of ignoring it.  There are lots of ways to handle it; it's a frequent topic in the MemoryCaregivers support group meetings.   Knowing what to watch for, and how to introduce the subject, is important in making the transition. It's not too early to be starting this process - a $20 lottery ticket seems pretty mild when you compare it to what could happen if he's in an automobile accident. 

As you are finding out, living with a person who has memory loss, even in its mild stage, can be challengting.  Perhaps one of the most important things you can do is also one of the most difficult:  try to be patient.  Recognize that most of the behaviors you are dealing with are coming from the disease, not from him.   It's up to you to find the solutions.  One of the best things you can do to help yourself is to find out how other people in your situation are dealing with these same challenges.   Remember, you don't have to go through this alone!