Chelsea signed Mendy on a £22million deal from Rennes on Thursday after Lampard lost faith in Arrizabalaga following a string of high-profile mistakes.
Arrizabalaga, the world’s most expensive goalkeeper after Chelsea paid £71.6million for him two years ago, has been linked with loan moves to clubs in Spain and Italy.
The Spaniard could have to leave Chelsea to rebuild his confidence and resurrect his career away from the spotlight.
Lampard has revealed he plans to speak to Arrizabalaga before Saturday's trip to West Brom, with the coach confirming the game comes too early for Mendy to start.
“I will have a conversation with him and Willy Caballero over the next 24 hours or so,” said Lampard on Friday. “I have an open line of communication with both of them.
“I have not spoken to Kepa since the [Mendy] announcement. We trained and I did not see him.
“It is important as goalkeepers that they have their own small union on the training ground because of the nature of the way they work together. There is good competition there now and that is how we move forward.”
Lampard also revealed Chelsea will have to manage Christian Pulisic carefully because of concerns over his recent injury record.
Pulisic has missed the start of the season with the hamstring injury he suffered in last season’s FA Cup Final and had fitness issues last season.
The American remains sidelined for Saturday’s trip to West Brom.
Lampard said: “There is always a concern about a players’ fitness when the history says there have been some injuries, and last season we did have them with Christian.
“Of course when you look at a player with his recent record you are trying to find a way and a balance to get the best out of him, which you saw in big periods last year, and making sure you do not overcook him and leave him susceptible to injury.
“Particularly a player of his explosive pace and balance. It is a fine line. Christian is very open to that. He wants to play and is very nearly fit now, but it is something we will have to manage with him this season.
“We have all seen his talent and it something we want to get right. I am not saying it is a chronic issue, it is not, but we want to get as many minutes of Christian on the pitch."