It's been a tiny while since we stayed at BWI, they've since changed the restaurant downstairs, but most CL's are now the same. Over time, all CL's have transitioned form glass bottles of Evian, to a water dispenser that has Natura brand water. If you look at lounge images from the start of this thread you'll see what I mean. The image from the Beach club has a clear image. Some of the lougnes have slightly different style dispensers. Since the Innkeepr's club was remodeled, it is almost certainly has something similar to the Beach Club one.
Water is always a bit of a challenge for us too. One option is the on-WDW Hess stations. You won't even need a car! There is a Hess station next door to the Boardwalk hotel. (corner of Buena Vista DR) Hess has basic brands like Dasani. On property, Car Care Centre Hess has the widest selection of brands.
Other options: I haven't done this in a while, but Costco used to deliver bottled water. (but I think BWK charges a package fee, as it has business customers) If we have a car, another option is to stop at the Whole Foods, just off I-4 coming from the airport (use north exit, take Sand Lake Rd exit them make quick u-trn). WF has more high end brands of water. It is alsoa great place to stop for a snack or meal. They have a large hot/cold bar, tons of soups, a fresh juice bar, etc. There are also several Publix around.
Other folks like to use their own water bottles, and the kind with a built in filter is popular. (Brita?) We tend to just use disposable bottles and refill them a bit. I also bring a short Sharpie marker to label them. If you are a
DDP package, you could also use your refillable mugs.