It is not used that way. "throw Up" is used to mean "to vomit". However, bring up is literally to bring something up. e.g. 1. Why didn't you bring up the topic of taxes during the discussion ? (bring up = introduce as part of the discussion) 2. A. Where is your lunch ? B. It is downstairs A. Then bring up your lunch. Let's have it together

It doesn't mean anything special, I'm guessing that here, "up" is being used as a "directional complement", so it depends on the context. 要看情況、語境才能確定 譬如說，假如你在樓下，我在樓上，我會對你說：「待你的午餐上來，跟我一起吃飯」 - "Bring your lunch up (或upstairs) and let's eat together“. 這個"up" 跟「上來」的「上」 一樣。 I would usually never use 'bring up' to mean vomit, it sounds perhaps either chiefly British (英式英語）or archaic. We might understand it in context, but in a single sentence like this, I'm not sure we would understand you really meant "throw up" (vomit).

I have definitely heard/read "bring up" used as a synonym to "vomit". It's a genteel, polite alternative... Vomit / puke sounds rough and very graphic ... Bring up sounds more discrete, like a euphemism...

Forget the word "up". The phrase "bring your lunch" is a rejoinder to indicate a task might take some unexpected effort and time, so you should prepare by taking along some sustenance. A common example follows. Speaker A: If you do that again, I will beat you to a pulp. Speaker B: Don't forget to bring your lunch.

I have also heard people use the phrase "bring up your lunch" as a way to say vomit.