After ther lappet moulted in a container in the garage, I put him back on the hawthorn tree. I had the lappet in a container because while moulting, he couldn't hold onto the branch and he fell off. Luckily, I noticed and put him in the container.
False alarm for the Buff tips - they aren't about to pupate. They did start eating, and the runny frass was a bit of mild diahorrea caused by rain on the foodplant.