Being a geologist, I can assure you that lava rock can be very sharp. It does depend on exactly what kind of lava rock you are on of course. But often as lava is erupted to form rock, it cools so quickly that it actually forms glass, which as you know is very sharp when broken. Out here in CA I've had to drive over some volcanic rock and was almost certian that I was going to come out with 4 flat tires but got lucky. On the flip side, it can be eroded and not be bad at all.
Where exactly are you wheeling? I may know more a bit more about the rock.