Lawal, who featured in the Super Eagles' largely unsuccessful World Cup campaign, opted for the move after failing to attract much interest from major clubs in Italy or Spain.
"It seems like a challenge to play for Levski," Lawal said.
"They have just won the league and I hope it will work out."
He added that he did expect any problems when it came to agreeing a deal with Levski.
"Everything is taken care of by agents," he said.
"I take it everything is in order, but it's only completely certain after I have signed."
Lawal has been playing in the Netherlands for six years, after previously being at Tunisian side ES Sahel.