Manchester United defender Evra described Lizarazu and three other television pundits as 'tramps' following France's win against Finland last week.
Evra has accused them of deliberately trying to tarnish his reputation while talking about him on French television.
Lizarazu responded by saying: "Evra blames us for dirtying his image but he is doing a great job himself."
Evra has had a chequered international career with France and has been heavily criticised for his role in a player revolt at the 2010 World Cup.
The 32-year-old was stripped of the captaincy and suspended for five games for his part in the revolt with many calling for the full-back to be banned for life.
France coach Didier Deschamps has tried to defend Evra's latest outburst, but admitted the player will never captain Les Bleus again while he remains in charge.
"Of course what Evra said is regrettable - but I'm not here to condemn anybody," Deschamps told Canal Plus.
"In the context of what has been said in the press it is difficult - I'm not saying he was right but it is difficult", he added.
"He knows that with me he will never be captain because I don't see him as a captain, but he still has a role to play."