Mid-last year bitbucket released support for automated aws lambda deployments. However, it seems that it only works for the most rudimentary of use cases.
My use case:
1) My lambda functions are too big to update the lambda function directly with a zip, I need to upload that zip to an s3 bucket first and then update the lambda function
2) I require quite a few python dependencies (numpy pandas etc) that need to be compiled on an awslinux docker image for them to work on lambda.
How are others managing automated deployment from bitbucket to aws lambda with a similar use case?
I would suggest taking a look at the Serverless Framework. It has a CLI tool that allows you to compose an entire Serverless service by configuring various managed services and Lambda together and then easily deploy with a single command: serverless deploy. This can then be used in something BitBucket Pipelines to automate deployment when changes to configuration have been made. 
Alternatively, I know the Serverless Framework has a CI/CD feature built into their Serverless Framework Pro dashboard that supports GitHub and will soon support BitBucket as well. 
If you need some help getting started they have a tone of learning materials and documentation at serverless.com
Bitbucket deployments no support for s3-based lambda functions