How can I change the default camera app (on lockscreen)? I would like to uninstall the default camera app and instead use the FOSS Open Camera. And I would also like to access the camera from the lockscreen.

How can I do this in Android 6?
Default camera is a system app, which requires root to uninstall default camera app. You can use Titanium Backup like app to remove system app (N.B: Removing system app will be harmful to your device). 
Settings->Security, under device security, tap on settings icon near screen lock. Select Lock screen shortcuts. Tap on any left or right default icons, prompts to choose action: tap on select application. Tap on Apps on top, and select your required camera app(These setting is on Lineage 14.1 android nougat)