It depends of the PoD.
Would the PoD itself be the invention of printing press, I would say that it would be too fast for a safe widespread anyway.
An earlier local production of paper in England is mandatory, but I won't see it being that quicker than IOTL. Maybe the XIVth century instead of the late XVth, admittedly.
With that, and without HYW, you may have an earlier printing press appearing around mid XIVth century, relativly plausibly outside England (maybe Upper Rhine) and being present in England between the latter half of XIV up to XV in some places.
Remember that first printing locations were essentially due to an inverstor presence, and patronage. It really took decades to have it being relativly widespread, understanding that almost all of these printings were outside "heterodoxial hands" but people close either to rulers, economic elite, clergy, etc.
Furthermore, the problem with Lollards was less how to widespread their ideas, than these being irreconciliable with the contemporary society or at least powerful elites. Not that a more widespread presence of written texts would hurt of course, but literacy being essentially a clerical thing outside rulers. I could see urban patricians being more touched, but it doesn't look like they had enough military power on them.
At this point, as you seem to want to do it since some times, I'll advise you to not care about PoD plausibility that much, and to argue of an earlier invention in Frisia without HYW diverting ressources.
Part of me feels like it's incredibly unlikely because the press would have to not only be invented 150 years before OTL, it would also have to make it across the channel WITH paper abilities AND survive through the HYW AND the Bubonic Plague. I'm shooting for the freaking moon.