Hello. Is it possible to connect to limesdr via ethernet? Thanks.
Not as it is; however, it should be possible to do it via a “proxy” board. One could connect the LimeSDR to e.g. an Odroid XU4 with USB3 and then use SoapySDR with the built-in remote module.
I have not tried it but it sounds like an interesting experiment to try in the coming weeks 
I noticed the board images show a GPIO header for the FPGA. I’m hoping they are available for use by the user. Could they be used to wire in an ethernet module?
If there are sufficient pins for the device/module, I don’t see why not.
@n5fpp
Yes, there are 8 FPGA GPIOs available on the LimeSDR-USB board. Should be enough to connect SPI bus based WiFi/Ethernet module.