Inside of large companies, is it standard practice to use SSL (e.g. https) for running corporate apps over the LAN.
Generally SSL for LAN only internal applications is not common practice. Historically the LAN has been viewed as a "trusted" network, and so SSL for LAN apps hasn't been a priority.
Also, connection to internal application servers is usually via an authenticated proxy, which in itself mitigates some of the risk.
This is, slowly, changing however as organisations (generally) increasingly treat the LAN with less trust.
If not SSL, how is this security threat dealt with?
Most enterprises do monitor what is attached to their LAN and record events when new devices are added.
If the device doesn't correspond to something planned (i.e a new desktop or printer) - then it is investigated.
Unauthorised devices are seen as a much greater risk (than not using SSL) because they pose additional threats, like introducing a virus, an external network connection, or some other kind of attack vector.