Lukaku took his tally for the season in all competitions to 22 with his 17th Premier League strike of the campaign in the 3-1 victory over Aston Villa on Tuesday night.
The 22-year-old Belgian has scored at least 10 goals in each of his last four top-flight campaigns in England and is just two strikes behind Jamie Vardy in the race for this year's Golden Boot.
Former Nigerian forward Amokachi, who scored 14 goals and won the FA Cup in two years with the Toffees in the mid-1990s, believes Lukaku has all the attributes to be able to rise as high in his career as African legend Weah.
Amokachi told the BBC: "When I look at Lukaku I think of George Weah. He has the potential to be one of the best striker’s in the world.
"He is scoring goals but if he brings out that ruthlessness in him then he will be in the 30-goal-a-season goalscorer. He has the speed, the skills and good with his head also – what else do you need from a striker?
"All the qualities a striker possesses he has, so he just has to be a bit more ruthless to be among the best in the world."
Weah's career would certainly be a fine one to replicate - the 49-year-old scored 193 goals in 478 matches in Europe for Monaco, Paris Saint-Germain, AC Milan, Chelsea, Manchester City and Marseille.
The three-time African player of the year was also named both European and World footballer of the year during his first year with AC Milan.