In The Middle Parts of Fortune, a novel about World War I published in the 1920s, "as lief" is used by rural speakers from Dorset or Somerset.

At one time "lief," in the sense of prefering something, was standard English; I've seen a quote from Spenser using "lief or loth" as the equivalent of "willy nilly." It probably survived in rural and working class speech around the UK long after it passed out of upper and middle class usage. Since JA doesn't usually do dialect or regionalisms, I would guess "lief" or "lieve" was still standard English in her time.