Can I request a vegetarian meal?
Yes, there are hosts who can prepare a Japanese vegetarian meal and a few hosts are vegetarians.
You can find more about vegetarian cooking on this page.( https://airkitchen.jp/list/tokyo/vegetarian.php)
That said, not only are there hosts who may not be as familiar as others so being specific as possible as to what you can and cannot eat will be important.
This includes defining what type of vegetarian you are such as lacto-ovo-vegetarian, pescatarian, etc.