Is it possible to intercept kill signals to close DB connections right before a lambda function is killed and started cold?
There is no way to know when a lambda container will be destroyed unfortunately.
With that out of the way, cold boots and DB connections are both very discussed topics using Lambdas. Worst is that there is no definitive answer and should be handled on a use-case basis.
Personally, I think that the best way to go about this is to create connections and kill the idle ones based on a time out postgres side. For that I direct you to How to close idle connections in PostgreSQL automatically?
You might also want to fine tune how many lambdas you have running at any point in time. For this I would recommend setting a concurrency level in your lambda aws-docs. This way you limit the amount of running lambdas and potentially not drown your DB server with connections.
Jeremy Daly(serverless hero) has a great blog post on this. How To: Manage RDS Connections from AWS Lambda Serverless Functions
He also has a project, in node unfortunately, that is a wrapper around the mysql connection. This monitors the connection and automatically manages them like killing zombies serverless-mysql. You might find something similiar for python.
I dont think what you are looking for is possible at the moment. Hacks might work but I will advice not to depend on them as undocumented things can stop working at any point in time without notice in a closed source system.
I guess you are concerned about the number of new connection created by your lambda functions and the load it puts on the db server.
Have you seen pgbouncer (https://pgbouncer.github.io/) it is one of the famous connection poolers for postgres. I would recommend using something like pgbouncer in between your lambda function and db.
This will remove the load on your db server caused by creation of new connection as connections between pgbouncer and postgres can remain for a long time. The lambda functions can make new connection to pgbouncer which is more than capable of handling un-closed connections with the various timeout config settings.
Update on 9th Dec 2019
AWS recently announced RDS Proxy capable of connection pooling. Currently its in preview and has no support for postresql but they say its coming soon.
https://aws.amazon.com/rds/proxy/
https://aws.amazon.com/blogs/compute/using-amazon-rds-proxy-with-aws-lambda/