Staying within the laws of physics for our universe, this is not possible.
To injure, we need kinetic energy. Kinetic energy relies on motion - so a lightsaber has to be in motion to actually inflict damage.
Without motion, the only way to inflict damage is the energy of the plasma blade itself - which would just inflict burns on touch. Besides: to cut THROUGH something, you'd have to draw the line of the cut, at least.
In fact, thrusts would be the most harmless attacks - the wound is small and instantly cauterized. No internal bleeding, no gangrene ... If the thrust doesn't hit the heart, there's almost no chance of a finalizing injury. The most fatal - and most feared - wound in smallsword was the sucking chest wound.
Ok, well thought out and informed. But I feel the need to disagree about thrusting being negligible in it's lethality when used with a plasma blade that actively cauterizes the wounds it creates in real time. Thrusts and stabs are obscenely dangerous in this case especially. Though light sabers remove the bleeding to death part of the equation in comparison to traditional blade work, the "force required" to "cut" is the trade off which leads to my second point I'll share shortly. Mentally imagine defending yourself against a lightsaber while wielding one... the point is hard to deflect in motion, and many attacks or parries can easily transition into a thrust. So you now have a knife through butter ease of access to internal organs. Heart aside (talking human anatomy ignoring alien anatomies for the moment), severing major arteries precisely, damaging or destroying kidneys, liver, parts of brain without bisecting or decapitation, lungs, spine... one agile penetration of a few inches is lethal or debilitating to the point further combat is unlikely from the injured party.
Secondly, true kinetic energy must be applied to manipulate the weapon. But unlike the amounts needed for traditional blades to achieve cutting, ripping, hacking damage physical material produces separating other solid matter; the plasma beam must require less. The main focus of that energy in light saber combat is reaching the target, parrying other energy blades, blaster bolts, vibro blades, etc. It's more so a matter of direction and momentum/inertia than the concern of damage. In my mind it's like Count Dooku (hailed as one of the top duelists of the order) employing finesse and efficency to kill. A properly timed thrust into an opponent in motion could easily lead to them bisecting or dismembering themselves with their own inertia.
Third, plasma blade temperature. Much harder to debate since it's in our realm of theoretical physics trying to use something like this in small scale combat... but one thing I vaguely remember from the games sticks out. If I remember right (sure someone will correct me if I'm wrong) but a lightsaber has it's focusing crystal. Previously alluded to in a post on this topic, that crystal helps focus and (pretty sure) maintain a stable energy blade. So, here comes the logical leap I made. It is a controlled plasma blade, in a universe full of shielding and other containment technologies. They have navigated sub space routes for thousands of years, so lets just say waaaaaay advanced from our perspective technologically. So, in theory, the plasma heat contained within the blade may well exceed the ambient temperature by design/ out of necessity. Or to protect the wielder as much as bystanders. Hence (going with original Sith Red blade/crystal lore) the Sith modifying their blades to be "stronger" or more destructive could expand upon that idea. Since they want to generally harm their opponents and accept a higher level of (even continual) risk to themselves if the power gained is worth it. Sorry I veered a bit away from my point to make my point which is this... Upon contact with metal, organic matter, or various similar substances the light saber (by design) could automatically adjust containment or even heat output to achieve intended results. SO potentially design changes over millennia incorporated ideas like cutting through thicker metal by super heating it more than when slicing through a tree and accidentally setting it on fire through a design flaw in essence. It seems at least plausible to me, these warriors would modify their main weapon/tool to have this versatility.
My contribution to the conversation of these theories ends there for now. Dissenting from some while agreeing with others. Oh the joy of sparking the exchange of ideas, while attempting not to be senselessly rude or argumentative. At least that was the intention. I only desire to live long enough to see someone create a functional, handheld, true to traditional design, light saber!