The limitations of the PPP protocol can come into play
in L2TP. PPP packet payloads are encrypted, but keys are not
refreshed. This implies that someone listening to the traffic
for a long enough time can launch a dictionary-style attack
against the key, and thus gain the data.
In practice, an L2TP tunnel is an L2TP frame inside a UDP packet.
Because UDP is an IP protocol, we can apply IPSec to increase the
security of the dial-up VPN. This comes at the cost of administering
IPSec on a phone line; but L2TP is too easily compromised not to
consider adding a measure of security through IPSec or another
custom IP security framework.