Can cops lie if you ask them if they are a cop or an undercover cop?

Of course they can.  If they couldn't, criminals of all types would learn to ask this question and undercover work would become a thing of the past.

A few years ago in Howard County, MD, LE was having sex with the poviders at a massage parlor (during a sting). The cop lied. When it came up in the court system the DA lost bigtime.

What a huge misnomer.  My relative is a retired policeman who did work vice at times.  The police are ABSOLUTELY ALLOWED TO USE LIES.  In most cases they can't entrap you or expose themselves.  But asking them if they are LE is just plain silly!!