The Blues have already qualified for next season's Champions League by finishing fourth in the Premier League, but the Gunners must win at Wembley to qualify for the Europa League.
Lampard told BBC Football Focus: "I've heard how there's more on this game for Arsenal, and that idea worries me.
"We must put ourselves under pressure. This is a huge game for Chelsea."
Both Lampard and Arsenal counterpart Mikel Arteta can win their first managerial honours at Wembley - and both are on Football Focus from
Despite knowing they will be playing in Europe's elite club competition in 2020-21, Lampard - who won the FA Cup four times as a Chelsea player - says his squad must feel the pressure to deliver trophies to Stamford Bridge.
"It worries me that we as a club, as a team, think we achieved something last week by finishing in the top four," said the 42-year-old former England midfielder.
"We are happy with that but that's gone now. We don't consider what it means for Arsenal - we want to win the match.
"I've been in this game a fairly short time but I've played for many years and I know what I want the feeling to be around a final. It needs to be pressured; we need to be on edge. We cannot cruise into a final. You lose them that way.
"The feeling of losing as a manager is worse than as a player because you take on more responsibility - but the feeling of winning is better."
Lampard would not confirm whether Kepa Arrizabalaga or Willy Caballero will start in goal, but France midfielder N'Golo Kante and Brazil winger Willian are both available.
The 139th FA Cup final kicks off at 17:30 BST at Wembley and can be watched on BBC One, the iPlayer and the BBC Sport website.
This season's showpiece has been renamed the Heads Up FA Cup final to raise mental health awareness.