If all you need is the I&Q you could simply capture the I&Q from the LimeSDR and store it in a file. Most Zynq boards have SD cards for boot. You could make a partition and put your file there (or raw data in the partition if that’s easier) and write a program to stream it over the AXI bus into your FPGA.
If you need real time live I&Q you could switch the source from the SD card to USB. This is a bit more complex, but then you have at least developed and debugged the AXI streaming interface into the FPGA fabric.
Or if you want to test your Lime interface as well you could get the Lime FMC development kit as suggested by somebody else. Or you can try to get hold of a XTRX board which has a Xilinx Artix 7 connected to the Lime. Early bird/beta tester board owners might be willing to sell one.