I walked the Lebaniego in April 2019. i didn't get any snow, but a person told me it snowed one week after we were there.
September follows the European summer though (August being the hottest month). So the chance that you will get snow to the point of making a camino un-doable is extremelly small.
I got some info on Potes (on the Lebaniego) from a weather website:
"The average maximum daytime temperature in Potes in September lies at 21.8°C (71.24°F). The average minimum temperature goes down to around 11.2°C (52.16°F)."