Density of lava varies a small amount, but you can more or less handwave it as an average 2800kg/m3, which is roughly the density of Earth's crust. This is the important figure for your needs, because it is substantially higher than the density of humans, who can float in water, which has a density of about 1000kg/m3.
The second most important figure is viscosity, which not only varies quite a lot but is also quite hard to measure. There's a handy diagram in this paper on page 2 (labelled page 1517 in the document) which shows that some rhyolitic lavas can have a viscosity as high as 108Pa·s, whereas Komatiite lavas can be as fluid as 0.1Pa·s, equivalent to a very low viscosity motor oil. The extremely viscous lava is probably one you can walk across if you don't hang around (you'll still sink if you wait long enough), but those runnier lavas are a different matter altogether.
Here's a video of a man running up a small, high-viscosity lava flow on Mount Etna (alternatively, an article link with the video embedded in case you don't want to sign in to youtube). Etna mostly produces Andesite-type lavas, which are relatively viscous at 105Pa·s. Because the flow rate is low, an insulating crust forms on the top of the lava and he doesn't need a whole lot of protective gear. So lets assume that we only need to care about the less viscous lavas, as given your fancy protective gear you'd have no problem running around over the more viscous ones.
Now, Concrete has a viscosity of about 20-2000Pa·s, which is at the low end for most lavas. Concrete also has a density of about 2500kg/m3. So, can you walk across wet concrete? Well, you'll certainly sink into it to some extent whilst standing (see example in this video at 6m11) which does not bode well for your lava walking plans, at least as far as low viscosity lava goes. You won't be completely immersed of course, the density of the lava being what it is... your legs are about a third of your bodyweight so you'll sink up to your groin. You may be able to haul yourself out, if a crust is forming on the lava, but otherwise you're toast.
I have a plan B, though. Mud, of the sort you find in tidal mudflats is of a similar viscosity to wet concrete, though it has a much lower density (as low as 1200kg/m3 in some harbours). Wading through it in boots is an exhausting and often futile exercise, but this problem has been solved by various means including things called "splatchers" or, more boringly, mud-pattens. These are foot-square (or about 0.1m2) wooden slabs attached to your feet, preventing you from sinking into the mud. A lava-friendly equivalent, made of whatever magical material you have that lava does not adhere to, should serve you just fine. You might do well to carry some walking poles made of suitable refractory materials to help you balance. Remember that lava flows do in fact flow (lava lakes don't, but beware of gas bubbles forming) and you'll have to be careful not to be swept off your feet. For the least viscous lavas, you can solve the issue with bouyancy. A 32l hollow float will be quite enough to keep an 80kg person above the surface of the lava, so two big 15l boots would do though balancing may require quite a bit of practise... you might be better off with a paddleboard!
Note that lava is shear-thinning and thixotropic, meaning that under the right circumstances its viscosity will decrease. This contrasts with stuff like quicksand or cornstarch-water mixtures which are shear-thickening. Tricks that work on one may have quite the opposite effect on the other, so don't take those custard-walking videos as helpful advice in this situation! The correct gait will depend very much on the specific lava flow and temperature. For low viscosity flows, I suspect that running will increase the chance of Bad Things Happening, though it won't matter for very high viscosity lavas.
GrinningX's now deleted answer referenced surface tension; assuming they don't bring it back I'll briefly mention it here as it is passingly interesting and relevant (and feel free to ask me to delete this if the answer resurfaces).
Lava has a surface tension of 350mN/m to 370mN/m. Water has a surface tension of more like 72mN/M. That's only a 5-fold increase, so unless your lava-walker weighs no more than five times as much as big pondskater (the largest of which weighs a mighty 10 grams) they'll break the surface tension and they'll need to rely on bouyancy to save themselves.