What is turntable “liveliness”.

No such thing.  It's an old wive's tale.  Or worse an audiomyth.    Turntables don't matter much.  It's the cartridge. and the tonearm.  Try a different cartridge.  Or tonearm.  

Turntable sound might be the biggest money-hole crock in all of audiofooleya. Move the vinyl at a somewhat steady speed and do it quietly.  All a TT has to do.   Then the tonearm has to do it's thing for the cartridge.  

Oh, this talk about turntable sound has gotten me lively!  

But looking at a real expensive TT does make it sound better.  It better sound better.  

Disagree. Turntables make a big difference, but never to the exclusion of the effects of the tonearm/cartridge match. My listening experience suggests that the tonearm and cartridge should be considered as one. As a result, within limits of course, you cannot say this tonearm is better than that tonearm (if both are of high quality) without also stipulating the cartridge. Likewise, where two cartridges of similar excellence are concerned, a comparison is not believable unless they were auditioned in the same tonearm. On that background, the turntable has many additional important effects. The timekeeping function, just to begin with, should not be trivialized, because less accurate turntables are adding colorations due to their speed instability. In addition, the shape of the plinth itself and its build materials and its isolation from environmental perturbations have a significant effect on every aspect of the listening experience. 

I have been through Belt Drive, Idler Drive and Direct Drive TT's, of which I have come to settle with DD as my 'go to' design.

Additionally I have heard my TT in quite a few different systems where there have also been BD, ID or DD as the resident TT's.

I have no prejudice against other Drives, I have been impressed during my own ownership and through experiencing those owned by others.

I would say a ID TT, has it's feet firmly bedded in the substrate, and can be a experience, where the Bass Range can be very present, to the detriment of the MId's and Highs. I have experienced this to become much improved by the use of a off board Speed Controller, and have heard a range of Speed Controllers that are able to be quite perceivable on how they impact on the perception of Bass being present. 

Today I firmly believe the 'structure/materials' used for producing the TT and the method used to support the TT in the home environment are quite capable of impacting on the produced sonic for the better or the worse.   

Experiences have shown a certain design for a TA, that is quite a common design/geometry, can substantially inhibit the sonic and produce a subdued sound, that is seemingly on a leash/constrained. This in itself could create plenty of descriptions as an explanation for what an alternative and less constrained presentation from a different TA>TT can sound like.   

                                 What @lewm said, +1

                                      It's a, "system".

                                     Holism matters!