We do understand the meaning of End of this World. Lieberman is referring to this life and not the Hereafter. It is similar to "Free Hold" (ownership of real property), inherited or held for life. In other words, Jerusalem inherited by G-d to Jewish people as "Free Hold" (eternal) in this life. There is no such thing when Islam came into the picture then Jerusalem shall be under Muslims custodian. Even clear in the Quran saying that the land (Jerusalem) inherited to Jewish people and never mention at all to Arabs or Muslims. Jerusalem is not leasehold where property reverts to the Muslims when the lease expires. This is what Lieberman is referring as eternal (Free Hold) in this life.
Shaffir to Herzog: Opposition failed to show leadership in political battles against PM (Haaretz)
from the article: Lieberman: Jerusalem is our eternal capital, it will never be divided