When I try to run a python code on Lambda functions I got an error message related with regex module.

The error indicate that your deployment package is missing the regex dependency. To include it you should create a zip file that contains all dependencies. I would recommend using SAM to manage all the resources you need. Use sam init to create the project, sam build to build it, including all the dependencies, and sam deploy to deploy to your account.

Lambda requires you to prepare your own Lambda if it is not included in the standard modules.
You will need to create layers and upload the necessary modules as described in the following document.
https://docs.aws.amazon.com/lambda/latest/dg/configuration-layers.html