Having opened the tournament in Poland with a comfortable straight-sets victory over Germany, Brazil made it two wins from two against Tunisia.
Lucarelli top scored with 12 points in a one-sided encounter as Bernardo Rezende's side won 25-18 25-10 25-17 to maintain their unbeaten record.
The result kept Brazil - for whom Wallace and Lucas also led a strong attacking display - on top of Pool B, while taking their run to 27 wins from their last 31 World Championship matches.
However, the victors had cause for concern as captain Bruno was taken to hospital after injuring his right hand.
Bulgaria's quest for a first-ever World Championship gold suffered a blow in Pool C, though, as they were edged out 3-2 by Canada in arguably the game of the day.
Tsvetan Sokolov led the Europeans with 22 points - 19 coming from spikes - but that was not enough as Bulgaria went down 25-17 17-25 25-20 24-26 8-15.
Canada were forced to come from behind as they took the match into a fifth set, with Gavin Schmitt's 22-point contribution - along with his side's blocking game - ultimately proving decisive.
Schmitt played through the pain after shaking off fitness concerns to take his place in the side, and coach Glenn Hoag praised the 28-year-old.
"Gavin had some problems because of some injuries but the most important thing is that he was able, together with his team-mates, to manage and show their skills as a team," Hoag said.
"I think that made us win this match. Now we have to stay focused and score the maximum amount of points to advance to the next round."
Canada will next face Egypt, who lost in straight sets against Russia in Gdansk.
The Africans started well enough and were only just edged out in a tight opening set, but from there Russia's strength ultimately told as Dmitriy Ilinykh and Nikolay Pavlov combined for 24 points in a 25-22 25-15 25-15 win.
In the day's other Pool C match, China made it back-to-back wins as they beat Mexico in four sets.
Veteran spiker Yuan Zhi was the star of the show for the Chinese, contributing 30 points as they recovered from losing the first set to win 20-25 25-19 25-20 25-20.
Having started slowly, China gradually began to dominate. Geng Xin provided able support for Zhi at the net, with five scoring blocks from 11 attempts.
Brazil's most likely Pool B challengers are Finland, who also kept up their 100 per cent start in front of their colourful band of fans with a straight-sets victory over South Korea.
Meanwhile, Vital Heynen's Germany recovered from their opening defeat by posting a 25-16 25-21 25-19 win over Cuba.
