Can AWS Code Commit integrate with BitBucket without using lambda function

Hi, do you really mean CodeCommit or rather CodeBuild? CodeCommit and BitBucket are both flavors of git. So, I don't see what "integrate them" means

So, if you mean CodeBuild, yes: BitBucket can be integrated with it. See https://docs.aws.amazon.com/codebuild/latest/userguide/sample-bitbucket-pull-request.html