There are a couple of lounges that you might want to look at. Just a FYI, though, I have no experience buying a pass for these or using on arrival, as I have access through other means and DC is usually my final destination.
You can definitely buy a United Club pass- $59, and the t/c say that is same day arrivals/departures are eligible to purchase. In my experience these are average lounges.
Lounge Buddy looks like they will also sell access to the TK/LH lounges too. I have no experience with them or the LH lounge, but Turkish only asks me what airline I'm departing on when using my PP (they haven't asked for a BP yet). The Turkish lounge is very nice, and around lunchtime has some fairly solid offerings.
https://www.loungebuddy.com/IAD