That's a bug. Plz report it on the fpc bug tracker under rtl.
I simplified it somewhat, but it is repeatable:
program lasti;
uses sysutils;
const
txt = 'Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.';
begin
writeln(txt.LastIndexOf('ut').ToString); // IndexOf works correct.
end.
LastIndexOf is not working at all. And it is an FPC bug in sysutils, not Lazarus.