If you want solutions without holes, then wildBillMunson's answer of UITF/WXPY/VZLN is the only partition possible of the pentominoes into sets of 4 that form two of the same shape, though you actually have four options for the LZVN set:
If you allow holes, however, there are actually three more partitions of pentominoes into 3 sets that work: FLXY/IUTZ/VWPV, FTPZ/ILNW/VXUY, and FVNW/IUTZ/LYPX:
Some of those sets have more than one possible way to split them into pairs, but interestingly enough, LN-VZ is the only set of two pairs that can produce more than one final shape! All others have a unique solution.
Here's my Python code, if anyone is interested in how I got this. I'm not 100% convinced it's bug-free, so there might be extra configurations beyond the ones shown here.