Even fantasy lava is dense, but an adult red dragon has a Strength of 27 so I think it will work out fine. Heck, if a blue dragon can burrow through sand at 3mph, I'm thinking that locomotion through dense materials isn't a problem for dragons.
(Also, if it's still inside the volcano, I think it's technically magma?)
(Also, if it's still inside the volcano, I think it's technically magma?)