Those who know my nerdish ways will understand that it's taken me a while to respond to this question, because I felt it necessary to research our handling of all the element names.
Unfortunately, Tom Lehrer's song is not a definitive guide because, as he notes at the close of the song,
These are the only ones of which the news has come to Harvard,
And there may be many others, but they haven't been discarvard.
At any rate, as far as I can discover, there are only 16 chemical element names that we currently class as rare. We class as common the remaining 79 element names between 4 and 9 letters.
Lutetium is merely one of many rather obscure words in this group. (Of course, some of these quite long words will never appear in a puzzle, but I prefer that every word be given the correct classification as far as possible, since I don't know how I might want to use the word list in future.)
Set out below are the words I think should switch from common to rare, and those I think could remain as common. These proposals are based on my impressions of which words people are likely to have encountered outside the confines of chemistry class (and Tom Lehrer's song). I'd be happy to consider any suggested changes.
Switch to rare:actinium, americium, berkelium, beryllium, europium, fermium, francium, gallium, germanium, indium, lutetium, neptunium, niobium, nobelium, osmium, polonium, rhenium, rhodium, rubidium, ruthenium, samarium, scandium, selenium, tellurium, thallium, vanadium, ytterbium, yttrium
Leave as common:aluminium, aluminum, antimony, argon, arsenic, barium, bismuth, boron, bromine, cadmium, calcium, carbon, chlorine, chromium, cobalt, copper, fluorine, gold, helium, hydrogen, iodine, iridium, iron, krypton, lead, lithium, magnesium, manganese, mercury, neon, nickel, nitrogen, oxygen, palladium, platinum, plutonium, potassium, radium, radon, silicon, silver, sodium, strontium, sulfur, thorium, titanium, tungsten, uranium, xenon, zinc, zirconium