The 23-year-old scored his first goals for the Toffees since March – a run of 13 games – which followed his Belgium double in the recent international break.
Jermain Defoe had the best opportunity of a poor first half when the ball dropped into the box and he snatched his first-timed effort, lobbing over the crossbar from seven yards.
The overdue opener came on 60 minutes after Lukaku was left unmarked on an Everton counter, heading past young goalkeeper Jordan Pickford who had been impressive when called upon.
The former Chelsea forward went close minutes later when he drilled an effort against the crossbar after turning his man in the penalty area. But he soon added a second
Summer signing Yannick Bolasie showed his value – for the reported £25m fee paid to Crystal Palace for his services – as he set up the second, making a run to the byline, crossing for the Belgian to double his tally.
He nearly grabbed a fourth when he found space on the edge of the box, but he blasted the ball well over the bar.
Gerard Deulofeu nearly piled the misery on former Toffees boss David Moyes, as he beat a man before sliding the ball across goal and past the post with less than ten minutes to go.