If you didn't know it already, a Restricted Parking Zone has signs at the entrance streets that tell you that you can only park in marked bays. No yellow lines are part of an RPZ, and, in fact, councils should remove them as their presence would be confusing.
To get to Lord St West, (which is one-way), you would have had to drive down Cardwell Place, and would, therefore have passed this sign: -
https://maps.app.goo.gl/c1mdd9ifnHGPKrEB6Then, turning left from Corporation Street into Lord St West there is an RPZ repeater: -
https://maps.app.goo.gl/zPMWgcxdtNf4Qx6G9However, whilst it looks as if you are bang-to-rights, I do have my doubts about this RPZ, because the council have not fully removed the single and double-yellow lines, which makes for much confusion.
So, advice is not to rush and pay, but wait a bit for others to comment. Don't miss any deadlines on the PCN, though. I think if your case got to an adjudicator, there is an excellent chance of a win, because the council have failed to follow the signing requirements of an RPZ, namely leaving the yellow lines in position. JUst look at these double-yellow lines in Cardwell Place after passing the RPZ sign.
https://maps.app.goo.gl/fTSCFHR5usbkyWt76And finally, please post the PCN, all sides, so we can check it for errors.