We keep a portion of our caseload at any given time on a sliding-scale rate, funded partly by a small endowment and partly by clients who’ve chosen to pay full rate specifically to support it. The number of people who qualify and simply never ask is higher than you’d expect — a lot of clients assume a sliding scale is only for people in visible financial crisis, when in practice it covers a much wider range of situations.
The honest way to ask is just to ask, at consultation or any time after: “is a reduced rate something I could be considered for?” You don’t need to justify it beyond that in the first conversation.