I don't know what the announcements are at Lime St, but at Sheffield it something like "The xxxx (EMR) train to Liverpool is 45 mins late. Passengers for Stockport, Manchester, (other stations served by both), and Liverpool, your next fastest train is the xxxx (TPE) train to Liverpool Lime St".So Northern, TPE and EMR accept each other's tickets during disruption. But if, say, you were booked on an EMR train from Liverpool Lime Street to Manchester Oxford Road. You turn up at the station in plenty of time and find the EMR train is running 30 minutes late (for example). Could you then get a Northern or TPE train to arrive in Manchester less late, or do you just have to wait the extra time for your late train?
As no mention is made of ticketing restrictions, I take that to mean passengers intending to travel on the delayed train have been advised to catch the next timetabled one as it will leave before the delayed one. I would be more than willing to argue the point with any guard etc (and any subsequent correspondance) stating otherwise if I was affected but, to date, I have not been. Regular observation of on train interactions show that many passengers do not understand the nuances of ticketing and/or do not even realise they have operator restricted tickets.