it is less about density and more about viscosity, which depends on the type and temperature.
I had an opportunity to interact with lava during a Hawaii eruption, and people could run/walk across red hot and flowing lava, but it would start melting the bottom of your shoes. This lava was definitely on the colder end of the spectrum, with a consistency like bread dough.
On the the other end of the specturm, there are very hot low viscosity lavas similar in consistency to soup. If you tried to step on that, it would be like falling into a pool.
