There is currently no canon info about Zed being in a romantic relationship with anyone.
In the canon lore he hasn't even met Syndra or Ahri.
The reason why Syndra and Zed are listed as "related champions" is most likely because they have similar backstories and ideals.
Both had masters who disapproved of their powers and both ended up killing them(or at least this seems to be the case for Zed,we don't know what exactly happened there) and both think that the ionian traditions are limiting their potential.
So if those 2 were ever to meet(which is likely going to happen eventually),they'll likely make an alliance.