Death by lava is an often-used trope in films, most likely because of its slow, dramatic nature and the poetic beauty of being engulfed by liquid fire. But unfortunately as with so many things in the film world, most movie scenes depicting a person slowly sinking into lava until they are completely submerged is completely unscientific.
Lava is essentially molten rock. Just as ice and rock have different densities (try smashing two together for comparison), water and lava have completely different densities. In fact, lava is just over three times denser than water and somewhere between 100,000 to 1,000,000 times thicker (viscosity). The extremely high viscosity is why lava does not flow well, much like thick syrup and pitch. Density matters because less dense objects float when placed in a denser substance. Human beings are slightly denser than water (1010kg/m³ vs 1000kg/m³), meaning we can float if we have enough air in our lungs to provide the buoyancy. However, we are far less dense than molten lava. Even if we were as dense as lava, the extreme viscosity would make it very difficult for us to sink as the lava would not flow away from you that quickly. Ergo, if you were thrown into a pool of lava, you would not sink into a dramatic death.
Instead, you would most likely experience an even more horrific death as you stay afloat on the lava, as the surface of your body touching the lava is burned. Typical lava is between 1100~1200°C – well beyond the ignition point of human flesh. Not only will the skin, fat and muscle melt and peel away, but it will light up like a wick. The flame will soon cover the entire person and they will not only burn, but combust. Ultimately, only ash and completely dried up bone will be left floating on the lava, which will also end up igniting eventually.
Unfortunately, objects made of material such as steel and most other metals are denser than lava. This means that the Terminator would actually sink as dramatically as it did in the ending of Terminator 2 if he were to descend into a pool of lava.
(NB: It is important to note that in the movie, he descends into a vat of molten steel, not lava. Therefore, the accuracy of that scene hinges on whether the Terminator is made of a metal alloy denser than molten steel)