Lambda with stored procedures in RDS

RDS Proxy is available only for Amazon Aurora with MySQL compatibility, Amazon Aurora with PostgreSQL compatibility, Amazon RDS for MariaDB, Amazon RDS for MySQL, and Amazon RDS for PostgreSQL.

If you are trying to connect to RDS MSSQL Server, then RDS proxy won't work. In that case you will use whatever mechanism you are using today.

I could not find a blog post but here is a video that shows how to connect to RDS MSSQL Server from a .NET Lambda function - https://www.youtube.com/watch?v=LDGgAkSf8-Y

Lambda proxy config can be used to set a connection between lambda and rds

Simply that relies on vpc connectivity so you need a vpc attached lambda function

The rds sg must let your lambda subnet talks to rds, based on documentation the lambda and rds must be in same vpc and subnet , but I m sure there is other walk-around for that with separate tiers

Here the aws blog: https://aws.amazon.com/blogs/compute/using-amazon-rds-proxy-with-aws-lambda/