I wouldn't say walk in the park. The issue at hand is the fact that this is a workplace pickup and it's something I don't really have much experience with at all. I don't think I've ever actually asked out a co-worker since my teenage days working as a cashier at a supermarket. This here is a much different ballgame imo. It would obviously be a lot easier if she gave me all sorts of IOI's or even hinted at going out but there's been nothing of the sort. Only very nice conversations, tons of laughs and smiles, and while that might sound good on paper, still poses as an uphill battle once you are within the confines of the workplace. Because you see, even if she rejects me, I want to do this in such a way that I don't look like a goof and we can just move on like it almost never happened.
You're making this a bigger deal than it needs to be. The more pressure you add, the more significant the issue becomes for both of you. If you had enough experience with dating, you’d realize how insignificant asking someone out can be and how frustrating it is to go on a lunch date, especially when you're not genuinely interested. Women are often better versed in this game, and if they reject you, they typically act like nothing has happened as long as you get the hint and stop pushing.
But I digress, you can text her something like this on a Monday or Tue through your company’s instant messenger system:
You: Hi [her name], how are you?
Her: Hi [your name], I am doing good and you?
You: I am good! Haven’t seen you for a while.
Her: [BS excuse]
You: I forgot you still worked here. It’s like you disappeared and became a ghost lol j/k
Her: [laughs at the joke]
You: I heard you got a promotion
Her: [Says she did]
You: How is it?
Her: [explains what happens]
You: Well I guess I have to follow through with my end of the deal and take you to lunch. There are some chain restaurants not too far from here where we can meet up. Not sure if you know any around here.
Her: [mentions some or maybe doesn’t]
You: Tell you what, let go to [chain restaurant] on Thursday at 1:00 pm. We can drive in our cars and meet there. My treat. I know you are busy so let me know if you can’t make it.
Her: ok talk to you then.
If she rejects you:
You: Hi [your name], are you still down for today’s lunch?
Her: Hi [your name], I don’t think I can. I have a lot of meeting today
You: Really? Sounds difficult. What are they about?
Her: [BS thing about the meetings]
You: Ouch. Poor you lol it is all good. Maybe some other time. Good luck with the meetings and catch you the flip side. Take care.
Not sure how butt hurt you be if she rejects you, but it will certainly come one in your behaviour and body language. I’d personally would act like nothing happened.