Transferring Master to Master, different country/ LOR issue
Imagine for a moment that you are a trailing spouse.  You have fallen in love with someone with a job in City X, and s/he is not in a position to relocate.  Transfers in this case happen all the time, and there would be very little difficulty in asking for a letter of recommendation (LOR).

I suggest you say to your supervisor, "I love the coursework here and I love working with you, but it's become necessary for me to transfer to City X for personal reasons.  Would you be comfortable writing me a letter of recommendation for University X?"

If you have a close relationship with your supervisor, and s/he asks you what the personal reasons are, AND IF YOU WANT TO REVEAL MORE INFORMATION, then you can add, "the culture and surroundings here are just torturing me."  But probably it would be best to leave this out, especially if you are not 100% certain your supervisor will not spread your comments around.

Bravo to you for taking care of yourself.