Right now you cannot on iOS but you can on Android. Recently Google decided to take it out of the app and into your phone's settings.
So first you need to go to your phone's settings and then find Forza in your list of apps.
From there select notifications then find the notification you want to change the sound of e.g. Line Ups. Next press Advanced and then 'Sound' from there you will see a list of the all the options.
Please note that if you change the sound you currently cannot change it back to the Forza default. However we are working on changing this!
Here is a video showing how to do it: