I'm recently trying to set up a Minecraft server on Pi 2 either, ran into the same "can't catch up" warnings either. I can't even punch a tree smoothly. And after some time, the server crash due to slow performance.
The solution I found is that do not use a vanilla server from https://minecraft.net/download
, as it includes a watchdog program who kills the server if it takes 60 sec to do a "tick". Pi is slow, it will use more time to tick. Instead, get a Spigot server from http://getspigot.org/
I'm new to the Minecraft world, so can't tell if Spigot could handle everything on a Pi 2. For now, I'm happy with punching a tree fluently.