Does inactivating a line of business prohibit you from processing historical transactions associated with the line of businesses?

I'm assuming you're talking about departments/classes/locations/custom segments and you've renamed one of those to "line of business". But no, all inactivating records does is hide them from global search (depending on your preference settings) and restrict them from being selected on any dropdowns referencing that list/record.

Hi James, yes we renamed location to line of business. Thank you for confirming that there will be no impact on transactions referring inactive locations (aka LOB).