Acids from lemons and limes can improve the shelf life of some foods by inhibiting bacterial growth. Pickling is a common example of this (acetic acid though rather than citric or ascorbic acid).

There is no evidence that eating these foods will do anything to any bacteria in your body. Your stomach already contains an impressive amount of digestive acid and your gut is fully colonized by a significant biome of bacteria that you would not want to kill. Eating a lemon isn't going to do anything.

But even if it did, colds are not actually caused by bacteria. They're caused by viruses.

If you want advice on how to prevent or recover from illness more quickly, please talk to your doctor and don't listen to random people on social media. That's the lesson you should take away from this. All of this junk about raw honey and vitamin C is just that: junk medicine.