And pray that the staff there (or at whatever office you use) are willing and able to do that) or you could end up having to buy another ticket to your next port of call - and that would complicate things trying to use 2 tickets to exchange.
Condition 3 states:
"3. Where the full range of tickets is not available
If you cannot buy an appropriate ticket for the journey you want to make because the
range of tickets that is available at the station from which you intend to start your journey
is restricted, you must buy a ticket or Permit to Travel before you travel that entitles you to
make at least part of the journey. You must then, as soon as is reasonably practicable, buy
an appropriate ticket to complete your journey. In these circumstances, you only need to
pay the fare that you would have paid if you had bought a ticket immediately before your
journey. The price you will have to pay will be reduced by the amount paid for the ticket or
Permit to Travel."
http://www.nationalrail.co.uk/static/documents/content/NRCOC.pdf
So, the booking office at your origin can't sell the appropriate ticket, thus the range of tickets available is clearly restricted.
You buy a ticket to make part of the journey.
You get to Lime St. If the staff are not willing or able, then surely it is not reasonably practicable to buy the rover at Lime Street, given that you would only need to pay the difference in fair. Thus, as I see it, in this position you are free to move onto the next reasonable potential opportunity to perform the transaction.