There are no issues connecting two FPGAs directly, on the same or different boards, using LVDS, providing you've terminated the lines as necessary. Unless you're driving a significant distance there's no need for any external transceivers.
--- Quote Start ---
strange behavior that is reflected by low impedance (few ohms) between the LVDS signal (usually the negative line) and GND
--- Quote End ---
How are you measuring this? Assuming the board(s) is(are) off then the FPGA isn't going to know that it's supposed to be driving/receiving LVDS. However, you certainly shouldn't be measuring a low impedance to GND from either trace. So, I'd be looking for a board/build issue. If your board is on and operating then you're likely to be able to detect a low impedance path to GND depending on the state of the lines - that's more or less how LVDS works.
Cheers,
Alex