It won't really matter whether it's Lloyds or TSB that gets the Avios credit card. You should still be able to apply for the card in Scotland whoever operates it.
I have a LTSB credit card (not Avios) that I've not used for a long time and got a letter saying it was transferring to TSB. But that might be because my accounts with them all originate from when it was originally TSB.
Before the merger were there no TSB branches in Scotland? As far as I know it's simply a case of all the old TSB branches (sort code 77-xx-xx) will split off and the ones that were originally Lloyds will stay.
EDIT: Are the Lloyds branches still going to be called Lloyds TSB?