Yes, you can swap the positive (p) and negative (n) signals of a differential pair, but the resulting signal sent to the core logic will be inverted. The actual positive and negative pins can not be physically swapped, the signals must be inverted internally in the device.
If you are just using LVDS inputs and outputs without ALTLVDS SERDES, you can insert inverters on the core logic side. However, if you are using the ALTLVDS SERDES, you cannot invert the signal prior to the SERDES. That means, you would have to invert the signal on the parallel side. Depending on the number of channels in the interface, you may have to invert portions of the parallel word to set the data correctly.
If you are using transceivers, some protocols allow for (p) and (n) signal swapping, such as PCI Express. Similar to the non-transceiver I/O differential buffers, if you use a protocol that does not allow for (p) and (n) signal swapping, the transceivers will simply pass inverted data to the core and you must manually invert the signal. Refer to the respective device family handbook for further information on protocol support and transmitter polarity inversion options.