SchemaValidator is a property/setting of the APIGateway not of the Lambda, so having a Lambda in a different stack, makes no difference.
In the stacks where the lambda is defined there will be no mention of the gateway api. In the stack where you create the gateway api, yes, you need to reference/import you lambda in order to create the lambdaIntegration.
new apigateway.LambdaIntegration(myLambda)
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SchemaValidator is a property/setting of the APIGateway not of the Lambda, so having a Lambda in a different stack, makes no difference.
In the stacks where the lambda is defined there will be no mention of the gateway api. In the stack where you create the gateway api, yes, you need to reference/import you lambda in order to create the lambdaIntegration.
new apigateway.LambdaIntegration(myLambda)