Some years ago, my English was not perfect, and I usually told my office collegaues that "I go out for lunch" -- obvious not meaning partying, drinking or anything like that, but only referring to the fact that I am not going to eat in the office canteen, but leave our office building and get lunch somewhere else. Obviously, I learnt this is just wrong, and started better expressing myself. Somehow this expression popped up again and left me wondering how one can properly express a sitation where you state that you leave the building and have/buy your lunch outside of the building. How would you say that, without paraphrasing or otherwise making the sentence more complex? Would say "I am going outside to get lunch" or something like that be correct?

Natural English is eg I'm going out for lunch.

'outside the building' will be assumed by the listeners.

'to get lunch' suggests that you are going to buy some lunch and bring it back to eat in the office.