The Hammers have beaten Everton just once in their last 17 meetings, and that victory came on penalties following a 2-2 draw in the FA Cup last season.
Pivotal to the Toffees' most recent successes against West Ham has been Lukaku, who has scored in each of the last six meetings between the teams.
Yet Bilic's side have already ended one Merseyside curse this season when they won at Liverpool for the first time in 50 years.
And the Upton Park boss believes they can halt their drought against Everton - as long as they keep the Belgium striker quiet.
"That is more important than 17 games," said Bilic
"He's scored in six games out of six against us
But that only proves how good he is as a player.
"They have some great players with experience, legs, width, pace, imagination - the likes of Ross Barkley.
"But if you have to take one player out, then I wouldn't like to play against Lukaku because he is a top striker and gets assists, and that's why they paid 30-odd million for him.
"But we have great defenders and we've already stopped some of the great names this season with the help of the other guys in front of them.
"I didn't know it was that long since we beat them the last time, but that only shows what we are facing; a big club with the mentality of a club that has had its ups and down over the years.
"It's a club thinking big, acting big by signing players and by not letting players go, a massive club.
"So I didn't know it had been eight years
But that doesn't mean a lot
It's a new game
We beat so many big teams this season but that didn't mean a lot when we lost against Watford last week."
Saturday's clash is a meeting between Bilic's two former clubs in England
The Croatian defender joined Everton from the Hammers for £4.5million in 1997 and played under the late Howard Kendall at Goodison.
"Will it be a special game? On one hand, yes," he added
"It's a game against a big team in the Premier League and it's a great test for us.
"On the other hand it is special because I played there
Some of the people are still there so I am looking forward to it.
"I didn't play for 10 clubs here, I played for two, and one was Everton."
Source : PA
Source: PA