I should add to this that I'm in Scotland- AND that our Lemon Tree will reside in the Conservatory (when it's warm enough!)

Welcome!
I would pick them. They are only a slow drain on the tree's vitality, and will make it harder for it to adapt to its new home. Don't be surprised if they are kind of dry and tasteless--lemons are usually at their peak in October, so they are probably severely overripe. Be sure to give it as much light as possible until it goes into the conservatory, and you might want to consider moving it early. Darkness is usually more damaging to citrus than minor cold. Of course, if temps in the conservatory are dropping below -2 deg. C, that might still be a bigger problem!