I can’t speak to the actual physics of all that’s involved with lively v. damp - but I’ve given this some thought -- and the history of ski manufacturers dealing with this is long and involved.
Wood laminate cores traditionally were known for their lively characteristics - with the trade-off being the natural resonance of the material, and thus - chattering (which IS an aspect of “lively!”). The whole battle against chatter has resulted, over the decades, in some unusual - and many unsuccessful - mechanisms and devices!
The first was the addition of a metal layer. Before lightweight alloys, metal added so much weight to skis (anyone remember the Head Standard?), they were borderline unskiable. Devices and strange looking items got added to tips to combat chatter.
The K2 4, one of the legendary early “shapes,” had an LED light just forward of the binding toe, which actually LIT UP when “anti-vibration” was in effect. To this day, I have no idea what exactly what involved with that ski’s construction. (But the red light sure was fun when night skiing!)
Enter Titanal, a very lightweight alloy (and no, it’s NOT very much titanium at all, or your skis would cost THOUSANDS of dollars) that is mostly aluminum. Again, it adds weight, but far less than previous alloy attempts. Rossignol has recently ventured into using basalt, a natural material - but, in fact, it is a woven material that contains it in small amounts.
The road to retaining “lively” ski characteristics AND reducing chatter has been a very long one - even a period of injected form cores, then laminates of foam. Some ski manufacturers still use a measure of foam in cores, but it has largely fallen out of favor to its eventual breakdown.
I recently had an interesting side-by-side opportunity, in skiing a slightly older version of a ski I own that has no Titanal. Hadn’t skied it in a couple of years. DID find the chatter point in it (and was frankly put off!). The newer version does not, at least where and how I ski, have this same chatter point, does have a Titanal layer. It has a slightly higher swing weight but no major change in snow feel.
So I’ll venture to say that “lively” has everything to do with the actual internal construction of the ski, including type of laminate and other materials used to combat chatter.