One approach that I use, especially when I have to make several dough balls and I don't have enough refrigerator space to conveniently hold all the individual bowls or other containers, is to use zip-type storage/freezer bags. I put a little oil in the bag, drop a dough ball into the bag, and then roll and slosh the dough ball around until it is completely coated. That way I don't have to get my hands messy with oil. I then flatten the dough ball into a disk (by pressing against it from outside the bag) so that it will cool faster, which is important for a Lehmann dough. I squeeze out some of the air in the bag--but leave enough volume for expansion of the dough--and then zip the bag shut. At that point, you don't need much refrigerator space and you minimize the mass that is to be cooled.
I sometimes use empty bread bags to do the same, except that I twist and tuck the open end of the bag under the bag once I have put the dough ball (oiled) into the bag. Again, I allow enough space for dough expansion in the bag. You end up with a neat and compact package that uses little refrigerator space and, as with the zip-type bags, most of the cooling goes to cooling the dough rather than the container.
BTW, you can also use a light spray of canola oil from a spray can to coat the dough. When I do this, I spray the dough ball after I drop it into the container and then roll the dough ball around to get complete coating with the spray. If I am using a more typical container, such as a bowl, one trick I use is to take one of those freebie hotel plastic shower caps with the rubberized band and securely cover the bowl with it. Some of them are even transparent so that you can see what is happening to your dough. And they conform to most shapes and sizes of bowls you choose to use and they are reusable.