There is not sewage on my lawn any more.
Nor are there roots in the sewer pipe, thanks to the nice fellas in the quickly-dispatched utility truck. Yay city services! Also yay plumber who said on the phone "Where outside? Hm... try calling the city, they may take care of that for you." (Non-yay for the disconnected "if you are experiencing a sewer backup, call this number," but the woman who answered the main Public Works phone got me immediately transferred to the right place so that worked out okay.)