My Lock/Lak family comes from nearby Gruzdziai/Zagare, and I also have distant relations from Kursenai, who emigrated to South Africa.
One of the issues with that part of Lithuania is that the birth/marriage/death records no longer exist for the 1800s to early 1900s (lost or destroyed sometime around WW I). You can check the Routes to Roots website, in the Archives database, to see what records for the town are still available.
Re the Given name Aaron: I have relatives from that area who went by the Yiddish nickname Orel or Arel, for the Hebrew name Aharon. You could try searching on those. Also, after Lithuania became independent in 1920, the given name Aaron became 'Aronas'.
Re: possible original surname related to Arnott: I suspect it is a name that began with 'Ar' or 'Or'. You could check on Litvaksig or Jewishgen for surnames that begin this way. Using the Unified Search function on Jewishgen, searching for surnames that begin with 'Aro' only in the Siauliai district of Kovna Gubernia, I found Aronov, Aronovski, Aronson, Aronowitch, and more. For 'Ore', there was Orel, Orelowiich, etc.
And last - search on Jewishgen for all records that are the for town Kursenai. It's not that big of a town, and there won't be that many records to sort through. It's another way to see what surnames the residents of the town had.
And finally, though you already probably know this, back then a Hebrew teacher would be called a Melamed.
Lock/Lak/Lok and Kalon in Zagare/Joniskis, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine in Trenton, New Jersey and Lida/Minsk gub., Belarus