In 2006, Gaunce Lewis died at the age of 56. He'd done important work setting up equivariant stable homotopy theory, and I think it's fair to say his work was far ahead of its time. In recent years, thanks in part to the solution of the Kervaire Invariant One Problem by Hill, Hopkins, and Ravenel, interest in equivariant stable homotopy has blossomed.

Peter May wrote a wonderful memorial tribute to Lewis (and also Mark Steinberger). In a footnote on page 2 he writes

Unfortunately, much influential work of his in this direction remains unpublished.

The context is a sentence about Lewis's work on Mackey functors and "standard results, like projective implies flat for modules over a ring, can actually fail in such more general contexts."

I searched, but could not find any preprints of Gaunce Lewis online. His memorial page says he published 15 papers and the equivariant stable homotopy theory book (with co-authors). On arxiv, there are just two preprints, both with co-authors and both already published now. Hence my questions:

What was Lewis working on in the last years of his life? Are his ideas written down anywhere? Which ones have been worked out, and which ones are still open?