Would the Earth be lifeless? No. The Earth itself would remain warm from radioactive decay for billions of years, so microbes deep in the crust would survive. The oceans would freeze over, but they likely wouldn’t freeze solid. Tidal action, volcanism, and the aforementioned heat from the Earth’s core would likely keep some water liquid. Deep sea life, especially that around sea floor vents that don’t rely on the Sun, would very possibly survive or even thrive