The not found error makes it look as if live-stream-radio might not be on your path.
Rather than figuring out the details of your run environment, I suggest you 
simply specify the full path of that tool explicitly. If you're able to run the command from an interactive shell, then you can find out where it's located with the following:
which live-stream-radio
If the result is, say, /usr/local/bin/live-stream-radio, you'd simply add that to your script:
#!/bin/sh
trap "kill 0" SIGINT
while :; do
  /usr/local/bin/live-stream-radio --start myStream
done