I'm not sure where the author got this claim...it may just have been an assumption on his part, as many of the Eastern Algonquian languages died out long ago...not Lenape though. There were still a handful of native speakers left last I heard in the mid-90s--Lucy Parks Blalock "Touching Leaves Woman" was fluent in the Unami dialect, and she only passed away in 2000:
http://members.tripod.com/~lenapelady/lucy.html
As the obituary mentions, she had started classes in the language. I have a set of Lenape language lessons she made.
Oops...my bad. I got confused. Nora Thompson Dean was "Touching Leaves Woman"; she passed away in 1984.