Can I use an ethernet jack to send LVDS signals?
LVDS signals are generally incompatible with transformers/magnetics. The Texas Instruments application note does not have any examples of this sort.

Here is a similar discussion, see this Xilinx thread.

The LVDS will likely work over 100ft of RJ45/CATwhatever connection, you just need no magnetics and correct termination scheme on driver and receiver sides. However, hot plug/reconnect could be problematic due to possibility of cable charge up and ESD killing your driver/receivers.