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Rains have helped recoup lost water.
or
I would like to recoup lost time.
It seems to me that recoup is to regain something, thus lost would either be implied, or inclusive. So would saying "recoup lost ..." act like a double-negative, in that you're actually re-losing [something]?
I guess I am wondering if it is more proper to say:
Rains have helped recoup water.
or
I would like to recoup time.
One definition of recoup is indeed "to regain." As Webster's Third New International Dictionary (1986) puts it:
3: to get back: REGAIN ["an attempt to recoup his fortunes" —W.J. Ghent]
But another—and according to Webster's, earlier—definition has a different tendency:
2a: to make good (as expenses, losses) ["this is largely recouped to states from taxes" —John Kemp] : to make up for ["recouped their losses"]
The relevant version or portion of definition 2a for our purposes is "to make up for": You may lose water or lose time, but you can make up for those losses literally (by collecting water to replace the lost quantity) or figuratively (by making better use of your time going forward). In both instances, "recoup lost X" is not redundant or self-cancelling, any more than "compensate for lost X" is.
Incidentally, the "John Kemp" cited in the quotation associated with the first part of definition 2a is, I believe, the guy much better known to longtime U.S. football fans and Congress watchers as "Jack Kemp."
lost; however, I'd argue that it's not the same as compensate for.
Recoup means
1.to regain or make good (a financial or other loss)
2.tr to reimburse or compensate (someone), as for a loss
3.(law) to keep back (something due), having rightful claim to do so; withhold; deduct
While the term is often used in a gambling context, it can just as easily refer to an investment. Expenses are recouped even though they were not lost.
regain, not gain; thus, it's implied you already had it and not that you are obtaining it for the first time. While lost could mean it cannot be located, the maning can be extended to something once had, but no longer. Thus if you have money for expenses, it is lost once you pay for it.