[rtprjaew] Could we blow up to earth?

If we took all the deuterium and lithium on the earth's surface and crust and did fusion with it, would the energy released sum to more than the gravitational binding energy of the earth?  If not, how thick of a shell could be lifted to infinity? What smaller astronomical bodies could we blow up entirely?  Or, if the energy is more than enough to blow up earth, what larger bodies could we blow up instead?  Blowing up a gas giant avoids the need to bore a hole to the center.

(Why blow up a gas giant?  Because it's there of course.  Though the astroengineers can probably think of a better reason.  Maybe to get a clear shot at a moon on the far side with a rebel base.)

What if we used all the lithium and deuterium on and in the planet, not just the crust?  Though the process of extracting it might leave the planet pretty destroyed.  Which element is the limiting reagent?  If it is deuterium, can we effectively make more deuterium by fusing a neutron to protium?  What other elements can be straightforwardly fused to release energy (i.e., not iron) in a multi-stage thermonuclear bomb?

The original thought was, there is no known upper limit on how large and powerful we can make a thermonuclear bomb, especially one utilizing 3 or more stages.  Making one large one instead of many small ones is more efficient because the former only requires one primary fission bomb.  Of course fission could supplement fusion, but I suspect the total energy available on earth from fission is much less than from fusion.

Depict in science fiction scientifically accurate very large thermonuclear bombs, perhaps planet busters.