Just about every airline now participates with the major CRS systems using their "Direct or Total" access system where the display of seats is real time, real inventory. When a res agent or web system displays an availability screen it should be accurate as of the moment the request was made. If you (or an agent) sit for a few minutes or more before actually sending the request to actually book/reserve the seat the actual inventory can very well have changed so you get an "unavailable" response. This is especially true when viewing a display that shows only 1 or 2 seats for a particular class.
If you are looking for an L seat (god knows why if your on DL!) and it shows 0 and K and above are all at 7, I reccomend starting over, or waiting an hour and trying again. The yield management works in strange ways. I once saw 0 in L class, booked several full Y tickets, and the L inventory jumped to 4.
TW