Labour could hold on to leavers in a world where the tories weren't 'delivering brexit' and were telling people the kind of deal mattered. As soon as tories went 'brexit or bust' labour was gonna lose a lot of them. And labour's only value to remain was if it could bring leavers on board with a >
compromise. Once your voter coalition is remain-dominated there's nobody to compromise with so no point in acceoting weak sauce. Perfectly rational to vote lib dem at that point,since they are actually offering what you actually want.
Ps 'lying' was just the classic example of a strategy that works really well for a bit but when it stops working goes really bad really fast. I was just using in abstract sense. Not making accusations.