Lets assume the character in question is immune to fire/suffocation/crushing damage from being immersed/wading in lava. What is their RAW movement rate? Is it just "difficult terrain" for wading? Is it "swimming" for immersion? "Burrowing"?
I can homebrew an answer to this without difficulty, so I'm not looking for suggestions along those lines and I only want what the rules are. Answers should be backed up by rules citations.
Best Answer
Players would not sink into the lava.
In real life, if you were to trip and fall on lava you would not sink into it, but would rather lie on the top of the lava as you were cooked alive. This is because lava is denser (\$\rho=3000 kg/m³\$) than the human body (\$\rho=1000 kg/m^3\$)by a significant margin, even if said human is wearing heavy plate armor. Now if the character was a rock golem or warforged (\$\rho=7500 kg/m³\$) this would be a different story, as the rock golem would be roughly equal density and could swim while the warforged still would sink.
So it is not physically possible to swim through lava. But it might be similar to slogging through mud, depending on your weight and the size of your feet, how much you are carrying on your back, etc. It also could be possible due to the viscosity of lava for the average adventurer to run across the top of lava (especially if they are a monk) like some type of lizards run across the top of water. The biggest concern if you aren't immune to fire and the temperature is having your flesh melt from the heat. And you might want to do something to prevent dying from toxic fumes, namely sulfur dioxide.