Keane's no-nonsense attitude was most notable during his playing career when he walked out on the Republic of Ireland's 2002 World Cup campaign.
Lambert told the Daily Star: "He loves a laugh, he's not just serious.
"It's been great for me and everyone else at the club. It's been good."
Keane is Lambert's assistant with the Republic of Ireland national team as well as Premier League club Aston Villa.
The former Manchester United midfielder managed Sunderland and Ipswich Town but remains second in command to Lambert.