VEGETARIAN FOOD NEAR KOREATOWN
I don't think there's any strictly Vegetarian restuarants in Koreatown anymore. There was an all you can eat Korean Restuarant on Wilshire and Wilshire place a couple years ago, but the owners decided to change the menu to a more typical Korean place with meat dishes.
Slighty outisde of Koreatown is Pure Luck on Heliotrope and Melrose. I haven't been there in awhile , but I did like their BBQ Sandwich made from jackfruit with sweet potatoe fries. If you're still hungry, walk across the street and go to scoops where they serve ice cream with some vegan options as well..
Great suggestions. I would probably stick with Pure Luck and Scoops for dessert. However, if you can drive the five minutes up to Hollywood, there are tons of other places too, like Cruzer Pizza, Vegan Spot (if this still exists, I haven't been keeping up on things) and many thousands of vegan Thai joints (careful, not all of them are good about sourcing vegan ingredients). Also, Arax Falafel, isn't that far away, also in Hollywood.
In Koreatown, you can get bibimbap made without the meat/egg as well. That's my usual dish, since there are no vegetarian Korean places in LA, unlike in Seoul.