Evidently, there are some recipes for frozen confections based on oat milk.
For example, Dia Designs provides "5 vegan ice creams", most of which are based on oat milk. They read more like sorbet recipes, due to the lack of fat in the mix.
If you were to try to create your own oat milk based frozen dessert recipes, I would suggest modifying a base sorbet recipe, as they are not as dependent on fat as ice cream recipes. The additional starches in oat milk compared to water should add slightly more body and mouth feel, and make the product more opaque than a traditional sorbet.
If you are not opposed to egg whites, you might also consider using sherbert recipes as your base.
Note: the lactose in dairy products does not have a huge effect on the chemistry of ice cream (it is a small part of the total sugar in the mix), although it could potentially help inhibit sugar crystal formation somewhat (this is not usually an issue in frozen desserts). If you want to replace its effect, a small amount of honey, maple syrup, or even corn syrup would be very similar.