Even if it went through the ground without the hilt stopping it, it wouldn't go all the way through the earth. If you could theoretically drill a hole through the exact center of the planet, it'd be impossible to drop something all the way through to the other side because it would switch directions once it passed the center point.
Hasn't anyone come to the conclusion that as soon as it TOUCHES any lava at all, the saber handle would simply melt?
No handle, no light saber.
And lightsabers tend to switch off, the only person who has shown to keep his saber on was Darth Vader when he threw his saber at Luke - but it still switched off. He probably modified it so that he could throw it, because throwing you're lightsaber is obviously something Jedi's don't do. But as we know, Vader is evil and would want to use such a reckless and dangerous attack.
Also, even if the saber was somehow magically lava resistant (which they aren't, in Attack Of The Clones Anakin's gets wrecked by a machine), it would just stop at the Earths core and not budge.