Goncharenko's side head into the encounter at Dinamo Stadion third in Champions League Group F and looking to keep alive their tussle with Bayern Munich and Valencia for qualification to the knockout phase.
Having picked up six points from their first four games - to lie three points behind the top two - BATE can guarantee a Europa League spot with a draw, while a win would give them real hope of reaching the last 16 of Europe's premier club competition.
"It's hard to prepare for the national championship games," Goncharenko said at his post-match press conference after Saturday's 0-0 draw at Slavia-Mozyr. "And in the example of the match with Slavia-Mozyr that was clearly visible.
"As for the Champions League, we have repeatedly made sure that the team comes up with a different motivation. I have no doubt that tomorrow will be the same."
Lille coach Rudi Garcia will be expecting a big improvement from his team as they attempt to salvage some pride from a disappointing European campaign.
The French team have not yet picked up a point in the group - going down 6-1 at Bayern last time out - and must win by a greater margin than 3-1 in Minsk to have any hope of overtaking their opponents for third place.
But LOSC travel to Belarus on the back of Friday's 2-0 loss at Lorient - a result which left Garcia demanding answers.
"We had the opportunity to move among the top positions, but for the first time I did not see a team that wanted to be tied at the top of Ligue 1, and that is inexplicable," said Garcia, whose side have won just one of their last nine away games in all competitions.
"We'll see why the players completely missed the first half. I would understand. I hope that those on the pitch have an explanation, because I do not have.
"I am angry, yes, because I was expecting something else."
Neither team have any fresh injury concerns ahead of Tuesday's game.