does this mean that a PL3 can connect via LAN to a PC with Profilux Control
Yes

but also directly to the internet?
If you have a direct Internet LAN port:Yes (normally connection is done via a router; answer is also yes with router if it´s configured right)

If this is the case is it possible to remote connect directly to the PL3 from any internet acces point in the world and control the PL3?
If the right port is forwarded (10001 for PLC): Yes.