"I was nine years old. I remember my mum screaming in the house when we scored a goal. Afterwards, I knew third place was a big result," Lovren said of Croatia's 2-1 playoff win over the Netherlands in 1998.
"We can beat that, definitely, but we need luck. We have a good opponent in the next round, it will be difficult. There are no easy games here," he told reporters on Wednesday.
Croatia capped a splendid start to their World Cup campaign by beating Iceland 2-1 on Tuesday, making it three wins out of three to claim top spot in Group D, all while making nine changes to keep the team fresh for their next game with Denmark.
Lovren, who has worked under two of the key figures from his country's 1998 team - central defenders Slaven Bilic and Igor Stimac, says their influence has rubbed off on him, although he hopes his name will replace theirs in Croatian football history.
"I was lucky for both of them to be my coaches, so I have learnt from the best," added the Liverpool defender.
"Stimac and Bilic were maybe a little bit crazy, but you need to be crazy in our country. Nobody is normal. I’m not normal. They broke records, but I want to beat what they did. I want people to remember my name in the future, not theirs."
Lovren, who broke into the national team in 2009, is wary that Croatia also had a talented side in the 2014 World Cup, when they were knocked out of the group stage, and at Euro 2016, where they fell to Portugal in the last 16 in extra-time.
But he believes there is something in the air this time under coach Zlatko Dalic, whose side thrashed Argentina 3-0 and comfortably beat Nigeria 2-0 in their other games.
"We had big players in big leagues then and still we didn’t achieve anything. But I had a good feeling (about this World Cup) from the beginning," added Lovren.
"I feel it's totally different. On and off the pitch there is this strong commitment to each other. You can feel it.
"The manager has his own ideas and when he brings something new in and if he tells you he believes in you, then you will start to believe in yourself, and with that comes this atmosphere. It's amazing."
(Reporting by Richard Martin; Editing by Hugh Lawson)
