How do you ask people to a BD lunch?

Clueless senior (ish) associate here. I recently lateraled and for the first time have a BD budget (that expires in January and doesn’t roll). I’ve never done much before (other than helping partners put decks together).

I’m considering reaching out to some of the in house folks I worked with at my prior firm and asking if they might be interested in lunch. I might also ask some former colleagues that went in house. Is there any etiquette around how to do this? I’m not necessarily seeking out work (or think they have work to give me), I just liked working with them. Do I let them pick the place? Do I suggest a few places in budget? Do I have to specify that I’m treating them?

Any advice appreciated.

Edit: Super helpful! Thank you.

Author: Royal_Marzipan_6432