I do not think it is a good idea.
If you say that, it might indicate you are not mature enough to separate your personal and professional life.
I decided to leave my current position because she feels it is hard to maintain this relationship while we are working on the same team.
See, it's not the "organization" who has a problem - it's "you" (either or both of you). Before considering leaving the organization, try to talk to your partner about
- Why both of you working in the same organization / department is a problem / hardship?
- How you (or her) moving to other organization is going to solve the "problem" you have currently?
Honestly, before finalizing on moving out, try to find out the problem and the root cause of it.
Finally, if you want to move out, you don't need to lie either - just don't mention it. Find out a secondary reason for the shift and present that.
: I'm considering that there has been no event / incident in your current workplace which made you feel that the relationship is unwelcome.