Will a 3 LNB Direct TV dish work with a Dish Network receiver?

No, there is a receiver in between.

An LNB is a 'Low Noise Block'. The 'block' refers to a block of frequencies (not a magic box).

It is a low noise amplifier and converter. It changes the microwaves from the satellite signal, to a different, lower frequency that the satellite receiver can handle.

A voltage is usually put on the coax from the satellite box. This selects whether the polarized signal received by the LNB, is horizontal or vertical.