This is a novel way to think of volcanoes erupting, and the book already has me interested. Unfortunately, lava (or magma, as it's called when it's inside the earth) does not come from the earth's core, it's actually from spots in the mantle. Now, I say spots because the mantle is not all fluid-y and full of magma; the mantle is solid, as is everything down to the earth's core which is molten iron. There are places, however, that have the right variables to create magma spots, such as the Hawaiian Islands.
These sites explain it much better than I can, probably because they've researched it and such:
The earth has three main levels.
CRUST
MANTLE
CORE
Beneath the mantle is the earth's core.The Earth's core consist of a fluid outer core and a solid inner core.Because the outer core contains iron,when it flows it generates a magnetic field.This is the source of the Earth's magnetic field.