Which cells are you trying to culture? It will vary depending on origin, but when I cultured human bronchial epithelial cells, we typically would diisect the bronchii out, then use a non-specific protease to digest the cells from the matrix, followed by plating. You can sort the cells if necessary. The other option we used was explant culture (placing a piece of the tissue epithelial-side down in a culture plate with a little media) and allowing the epithelial cells to migrate onto the plate - explant works, but can be very slow and difficult to get a reasonable number of cells.
I attempted mouse lung epithelium a few times, but most of my experience is with human cells. Some of my colleagues have done mouse (see below for link on explant culture of mouse respiratory epithelium). The biggest issue was that the largest tissue source available was the mouse trachea - and it took a lot of trachea to get the cell numbers we needed. In general though, we were able to culture them by digesting the tissue with protease. With the human cells, the epithelium had much better attachment and growth on tissue culture plastic coated with collagen as a matrix (we used human placental collagen). Not sure what matrix to use with mouse.
One other thing we noticed with the human cells was that they did not subculture extremely well - after about 6-7 passages, we would notice morphological changes. I don't know if mouse cells would be similar. In our human model, we would seed the cells after protease digestion, allow them to proliferate for 3-5 days and them passage them directly on to transwell filters to differentiate them.
Attached is a Jove video I found on mouse epithelium culture from some of the people I worked with years ago. Hopefully it will be of some help to you.