I've been working with Lambda a lot more lately and it is not so bad... but also not great. I'm saying this cause I found it hard to have a git-first (or git ops) workflow that is good in AWS: it looks like everything is made to be changed manually. CloudFormation is a slow with some resources (if you need CloudFront it will take tens of minutes) and CodePipeline has a pretty terrible UX and user experience. CodePipeline is cheap and it works for sure, but it's not a good system for pipelines as restarting, terminating steps and getting the output of steps just don't work in a decent way (I want to see the output in the steps, not jump to CloudWatch). Pretty much every other system outside of AWS is better than that, but the integration with Lambda and APIGateway is not as good unfortunately. If you know of a better system for CI/CD with AWS Lambda outside of CodePipeline, I'd be interested to try it.
In a similar way, most of the serverless frameworks I've tried are written for a workflow that is executed from CLI which is great to start and attractive for developers but not good enough for a company that aims at full reproducibility of setups and "hands off" operations. Source code change should trigger changes in the Lambda/API Gateway setup all the time and it would be great if devs don't have to trigger changes manually.
Apart from those steps, I think Lambda is definitely promising and I see the company I'm working for right now using it more and more. The developer experience is still lacking IMO but I'm confident we'll get there at some point.