Karlach's early romance trigger is apparently bugged at the moment, so you can currently only start the romance at the party. I think, medium approval is enough. If you don't have any romances going, she'll be hitting on you pretty hard. If you already have one romance going, you have to chat her up. If you already have two romances going, your dance card is full and you cannot romance her. At least that's my experience, it might be wrong.
I am not sure if this derails the purpose of this thread too much but I would be very curious to read, what people would want from such a sexless romance or one that is not focused on it - which I personally find way more important.
