By offering you neighbor any money for ROOTS you just opened Pandora’s box.
Tell the person with the problem to get a licensed plumber to video THEIR sewer and have a LMP fix THEIR Problem. OR you will sue them for having raw sewerage come in contact with YOUR very exotic one of a kind living tree LOL.
Seriously if the sewer piping is in good condition roots should not have been able to get in end of story.