I doubt that will be a stopper for LRS, as it is legacy and you are not 'in-contract' for it. My problem preventing me from getting LRS is that my special deal Calling Plan is within a 12m contract.
However BT seem to mix up the diff 12m contracts. There could be 1 for the line rental which the recent BT Privacy + free Caller ID has imposed. There could also be a 12m contract on the Calling Plan. as I have. BT appear to be leaking that contract into the 12m LRS contract, when they would seem to be independant of each other.
You should try applying for LRS. By the time you get to 'Confirm' it should tell you whether or not you are eligible.
Bear in mind that with LRS, you go on to monthly paperless billing with whole bill monthly DDs.