As you all know, the LDB didnt truly defeat Alduin in Sovngarde. So will the LDB face Alduin again in the end of the Kalpa, and lose?

Will the Dragonborn lose? Probably not, considering Alduin is a weak sauce boss.

He's already gotten beat 2 times. Third Times a charm, but I doubt we'll ever see him again.

+1

Alduin be gone.

as far as we know, Dragonborns are not immortal (only reason Miraak was still alive is because he was basically in Stasis while in Apocrypha).

as such, I highly doubt the LDB would still be alive during the end of the Kalpa

Alduin's purpose is to devour the world. He was not destroyed because his purpose is not fulfilled. There are three future possibilities as to his return:

1. Alduin will return, and the Last Dragonborn will face him again.

2. Alduin will return, and a new Dragonborn will rise to face him. The Last Dragonborn will henceforth be known as the Penultimate Dragonborn.

3. Alduin will return, and be unopposed, and he will gobble up Nirn like a burrito.

I like the third one.