How to pass value of NODE_EXTRA_CA_CERTS to AWS Lambda deployed with Serverless?

I think this should definitely be possible in AWS Lambda.
There is an example on dev.to [1] which is similar to your use case. However, they are using .NET Core and the AWS SAM, but it should be easy to adapt the solution to serverless and Node.js.

Basically, you need two steps:

1. Create a Lambda layer which holds your additional certificate file [2][3]
2. Add the environment variable NODE_EXTRA_CA_CERTS to your serverless.yml and point the path at the file you uploaded in your Lambda layer [4]

References

[1] https://dev.to/leading-edje/aws-lambda-layer-for-private-certificates-465j
[2] https://www.serverless.com/plugins/serverless-layers
[3] https://www.serverless.com/blog/publish-aws-lambda-layers-serverless-framework
[4] https://www.serverless.com/blog/serverless-v1.2.0