If I’m starting a new catering business and use a popular brand of lemonade, rebottle it, re-label it and then sell it, is this legal?

IF there is no way for someone to know that you are using the popular brand--that is, as far as the customer knows, you made it yourself--then you have not violated the well-known brand's intellectual property  (e.g. it's trademark). IF there is no contract, agreement, or terms of sale which stops you from doing this (for example: when you buy the lemonade, there is nothing on the bottle saying "not for resale") and you did not lie to the company or its representatives as you buying it (that is, for example, you did not tell them you were buying a lot for a restaurant you owned, or your sports league, etc.), you could legally do this as far as the other company is concerned.

However, using their trademark; suggesting a connection with them that does not actually exist; using their brand to sell your own product (e.g. saying "Bob's lemonade is actually Well-known Brand's lemonade in a better  package); violating any terms of sale or other agreement; or lying to the other company in buying from them--doing any of these things would be illegal and would subject you to liability. This liability could include having to turn over *all* the money you made to them and paying their legal fees, too.

In addition, however, you could also face liability from or on behalf of customers, if you lie to them about the ingredients or don't post accurate ingredients on the label; you could also be violating various FTC-enforced labeling or advertising laws, and if your re-bottling is not sufficient sterile/clean/etc., possibly violating FDA laws about food preparation.

In short, this is a bad idea frought with risks and problems. And since you absolutely can't list that you are using the other company's lemonade--doing that, unless you had their permission, is the quickest and surest way to legal liability--it's unclear why you'd want to do this, as opposed to making your own lemonade.

Note that you could approach them or another lemondade manufacturer and see if they will produce lemonade for you to sell under your own brand: this is common in many industries. If you do this, while you'll pay them to manufacture, it will be completely legal--and paying for manufacture is likely no more (and in fact, is likely cheaper) than buying their product and repackaging it.