Network configuration always trips me up but I was wondering if the following would be possible.
I have an Amazon Echo Dot, which I would like to configure to say turn my TV on/off. My smart TV will take http requests with some XML, so when I am on my home Wifi I can do this.
What I want to achieve is to have a lambda function send my request and access my home network to do this. How would I go about allowing this to happen?
Yes, you can do this, and as you indicate, this is really a networking question - the ASK part of it is straight-forward.
You will need to open a port in the router that is connected to your modem and 'point' that port at your TV. Then you need some method for determining the IP address of that router, eg. get a static IP from your ISP or use something like dyndns. Now you can execute that HTTP command to control your TV from the Lambda that Amazon invokes when you speak your command to your echo.