In the context object of the Lambda, you can parse out some of the information you're looking for in the invoked_function_arn.
For example in Python: context.split(':')[3] will give you the region and context.split(':')[4] will give you the aws account id and context.split(':')[6] will give you the function name (which is also available in context.function_name
The invoked_function_arn looks like the following:
arn:aws:lambda:us-east-1:741063561123:function:lambda_context
Once you have that information you can use aws libraries (e.g. boto3 for Python) to get the rest of the information about the lambda (such as VPC, SG)