The assertion that GC systems may be faster than "manual" memory management is frequently made, but ill supported. In particular, it's easy and, in academia, encouraged to rig tests to avoid interacting badly with virtual memory. That's rarely so easy in Real Life.
"Eager", by the way, would be a more accurate moniker for what is normally done in C++, as there memory management, with the aid of destructors, is no wise more manual than in Lisp. Adopting the usage would allow GC promoters to hint at more honesty and scruples than their colleagues are inclined to exhibit.