Will the one who abandons prayer be eternally in Hell if he dies in that state, given the saying of the Messenger of Allah (peace and blessings be upon him) that the one who abandons prayer is a disbeliever?

The eternity of the prayer-abandoner in Hellfire varies according to the type of abandonment. One who abandons prayer out of denial is an apostate guilty of major disbelief (kufr akbar) and will remain eternally in Hellfire by scholarly consensus. As for one who abandons prayer out of laziness, the majority of jurists hold that their disbelief is minor (kufr asghar) and does not expel them from the fold of Islam; thus, they will not remain eternally in Hellfire. However, there is a narration from Ahmad indicating that their disbelief expels them from the fold of Islam, and this is supported by the apparent meanings of the texts.