oh hey I'd like to take you to lunch as a thanks for training me."
In Alan Rogers-Currie's book Mode One, he divided men's interaction with women into 4 modes :
Mode One - the rarest to Mode Four the extreme negative.
Your approach with this woman is very much described as Mode Two and with some of Mode Three - "I just want to be your friend")
""Mode Two:
Men who are saying what women want and expect to hear.
This man, although confident, is a man who wants to leave a good impression on women. This is the man who is overly concerned with getting women to like him and, therefore, will compliment women excessively and will be careful not to offend or challenge women. These men are timid, careful, afraid of criticism, too cautious, and indirect in their expression of their needs, wants, and desires.
They eventually tell women what they want and desire, but only after they are sure they are liked and won't be criticised; sometimes it's too slow and therefore can be too late, which will land them in the friend zone.
This is the type of conversation most women want to hear ( it's cartful, not intimidating, not challenging, and the compliments are a boost to their ego , but mostly because it'll leave them with the option to manipulate men), and that's what most women expect to hear because this is the conversational style of the vast majority of men. ( The simps)""
------
Go for it if you REALLY want to be her friend ONLY, but it reeks of simp if you're aiming for a romantic relationship/ connections of any kind, but pretend you only want to be her friend, and she knows it.
Stop playing games, be direct, confident , fearless.
As Atom Smasher used to say: stop playing the game - BE the game.