If an undercover law enforcement officer is asked the question "Are you a cop", do they have to answer truthfully, or are they allowed to lie? I'd think the 'standard practice' would be to lie about it just for the sake of their safety, but how would that affect the case they're building?

It's been answered already all over the internet. They can lie all they want. The usual argument is that it's entrapment for an undercover cop to ask you to sell them drugs. That has also been answered, it is not entrapment if they just ask you and you do it. They have to coerce you in some way, in order for it to be entrapment.

Here's one source but you can google several sources.

Does a police officer have to tell you he's a cop if you ask? http://criminal-law.freeadvice.com/criminal-law/drug_crimes/cop_arrested.htm

No. This is perfectly legal in most jurisdictions. Your question repeats one that is often asked, as people for some reason assume that dishonesty by a police officer should always lead to a dismissal. It is only police tactics that could deprive you of some constitutional right that will lead to suppression of evidence and a subsequent dismissal.

You didn’t use the word, but your question is centered around the legal doctrine of “entrapment,” but this term does NOT mean simply that you were tricked into getting caught. Entrapment means that the police persuaded you to commit a crime you had no intention of committing at the outset. In your case, you intended to buy the drugs all along. You just didn’t intend to get caught. There is no Constitutional right not to get caught committing a crime. What the police did was only to provide you with the “opportunity” to buy drugs, not to force you or convince you to do so.

If you had been approached by an undercover cop or civilian agent of the police and offered drugs, and you refused, but he came back repeatedly and urged you to take some, or used some sort of pressure or threats, then this might invalidate the arrest and result in the charges being dismissed. The reason behind this is that the law does not want police creating crime where there was none, in order to make an arrest.