Since Lorkhan's heart is part of Mundus,...

Does Alduin's eating of the world kill Lorkhan?

"And the Greedy Man always waves his arms about around this time as if to stop me just like you. It is almost as if you two work together to delay me. Is that what this is? Is some other low spirit hiding portions of the world while you two do this thing? Is this why the kalpa-feast always takes a little longer than it did the previous time?"

And then Alduin looked hard into the eyes of both the Greedy Man (far away) and the Leaper Demon King (close up), one of them for each eye of his own, and he knew it was so. These two spirits gulped big, and were caught.

"Oh crap," the Greedy Man said, "He knows my bargain with the king of leapers, I'd better hide under my mountain!" but he thought and said all this too fast and, without thinking, hid under his mountain even though its base had already been eaten and so it wasn't all still there. (This is how the Greedy Man became trapped both in and outside of kalpas.)

"Oh crap," said the Leaper Demon King, "You have found us out, World-Eater! Yes, just after the two bells of the All-Maker's Goat sound the Greedy Man and I and our servants hoard bits and bobs of the world so you can't eat it all. And when the world comes back we sort of just stick these portions back on and so that's why it is all bigger and bigger for you to eat each time.

Since Lorkhan's heart is part of Mundus,...

Does Alduin's eating of the world kill Lorkhan?

How can he be dead?

However, what people are neglecting to mention is that Shor/Shezarr does often come around as an avatar, like with Pelinal, King Wulfhart, and so on. He may be dead, but a god's death is different from a mortal's and a lesser daedroth's death.

This Creator-Trickster-Tester deity is in every Tamrielic mythic tradition. His most popular name is the Aldmeri "Lorkhan," or Doom Drum. He convinced or contrived the Original Spirits to bring about the creation of the Mortal Plane, upsetting the status quo much like his father Padomay had introduced instability into the universe in the Beginning Place. After the world is materialized, Lorkhan is separated from his divine center, sometimes involuntarily, and wanders the creation of the et'Ada.

The Nerevarine destroyed the enchantments on the heart, letting it return to its owner.

Why didn't it return to Lorkhan BEFORE the Dwemer dug it up and placed the enchantments on it?

No, Lorkhan is dead. Lorkhan sacrificed himself. A Shezarrine is not Lorkhan.

There is an effort to remove him as the hub of the Wheel. He's been killed before, once by the HoonDing and again by Vivec. Yet, he's the immortal, "Many Headed" Talos; he can die many times and live, as the heads on a hydra can be severed and regenerate. For Talos to be removed as the hub of the Wheel, the repetition of the Enantiomorph will need to stop.

Yes and no.

Lorkhan is not dead....you can't kill a god.
He is tied to mundas ,meaning he is not dead,is heart is hear.
If i remember right alduin/world eater also bound /threw himself to mundas. ( not 100% about this ).
To me it sounds like he is tied to nirn as much as lorkhan maybe,more so than the other aedra.

It would not make sense for that the be the case, because both of those characters have antithetical roles in the mythos to those who want to "kill Man.".