Jamieson, Fausset and Brown on Titus 1:2

2. In hope of eternal life--connected with the whole preceding sentence. That whereon rests my aim as an apostle to promote the elect's faith and full knowledge of the truth, is, "the hope of eternal life" (Tit 2:13; 3:7; Ac 23:6; 24:15; 28:20).

that cannot lie--(Ro 3:4; 11:29; He 6:18).

promised before the world began--a contracted expression for "purposed before the world began (literally, 'before the ages of time'), and promised actually in time," the promise springing from the eternal purpose; as in 2Ti 1:9, the gift of grace was the result of the eternal purpose "before the world began."