First, there are a couple types of pathologist that could have read the tissue sample. There are those that look at the vast majority of biopsies form all parts of the body and the ones that specialize in looking at oral tissues. In general either type can tell you if it's cancer. But the oral pathology community is much more able to parse the nuances of cellular changes that are unique to the oral environment.

Without seeing the report, my assumption is that when they call it atypic that the cell/s is/are changing in a way which they either cannot define adequately, or the changes are minor. But things might be evolving, or that a general pathologist read it and they are not accustomed to looking at abnormalities in oral cells. That's probably not very helpful as an answer. But I don't think calling something atypical is helpful either. All they have actually said is its not normal.

The good news for now is that isn't a finding of obvious malignancy. And that they want to deal with this through a laser ablation would mean that they have decided that it is superficial and not invasive. Meaning that a technology like laser can be used to burn off just a few surface cell layers of tissue and eradicate it all. That's a common procedure particularly with things that are not giant red flags. Leukoplakia is commonly removed in this manner as only about 25% pf them progress to dysplasia and only 25% of those go from dysplasia to malignancy.

Once this procedure is done, the tissue will be raw and sore, but heals up through secondary intent on its own. There is not suturing and the like because it's a superficial tissue removal.
No one can say if it will return or not, this will requires monitoring to ensure that if it does it is again dealt with promptly before it has a chance to prosper into something more.

Dentists and insurance are always a problem. They don't like to take medical insurance because of the paperwork, ditto Medicare. It's one of dentistrys shortcomings, which I will just say starts from their main lobbying professional society the ADA (who lobbied hard not to have dentistry covered by medicare, the age group that needs coverage more than any other. They spent millions of dollars and donations to politicians to see that it wasn't part of the Build Back Better plan. as did the Academy of General Dentistry.) and this isn't likely to change. This entire reply may be less than helpful, but there are no absolutes to comment on. I'd be happy to answer any further questions after the procedure if you post again. Brian