ANSWER: That part of the application that you must complete yourself (Applicant's Statement, Form 3112 A) requires several hours' work. However, getting the "Physician's Statement" (Form 3112 C) into just the right shape often takes weeks and sometimes months. Thereafter, the agency's bureaucracy can take an additional six to eight weeks before the application can be transmitted to OPM.
The timing of OPM's approval appears related largely to happenstance and apparently the whim and fancy of those running the show. For instance, OPM has no procedure whatsoever for expediting applications due to financial need. It claims to expedite the applications of the terminally ill on an ad hoc basis, irrespective of financial need, but refuses to expedite the applications of those threatened by financial ruin.
In my experience, case approval time varies from 10 weeks in a tiny minority of potentially news-sensitive cases (e.g. those concerning AIDS), to an average of five or six months. Some applications, however, languish inexplicably for a year or more, and have required complaints to the Inspector General to get the cases processed.
It may take up to several months, after winning, before you receive any money from OPM. By this time, if you've stopped working and are on LWOP, you will be owed a good deal of annuity back-payments. Usually, OPM makes an initial lump sum distribution of part of the back-payments owed. Thereafter, there may be another lump sum distribution of any other back-payments owed, usually together with the first of the regular monthly annuity payments.