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I haven't used Pulumi for Lambda but there are quite a few issues on Pulumi serialising functions.  <https://www.google.co.uk/search?q=typescript+pulumi+Error+serializing+function+site%3Agithub.com>

Last comment in this issue talks about building the Lambda outside Pulumi to avoid serialisation by Pulumi, which may help <https://github.com/pulumi/pulumi-aws/issues/2329>