Lump on gum under the tooth. I have a crown on - why is it there? Just noticed just that tooth always feels sensitive (Photo)

I am sorry to hear that you have a sensitive tooth. in my experience, there are several possible reasons for the painless lump on your gums. I think it would be a good idea to call your regular dentist and ask to be seen. I would let the dentist know that it is a painless bump and you don't know how long it has been there. The dentist will probably want to get one or two X-rays to see what is happening in that area. Taking a X-ray will show if the tooth with the crown has an infection or a crack in it, or whether or not the tooth has already had a root canal. 
Your dentist and hygienist probably did not notice the bump because it may not have been there at the time of your appointment. The dentist will likely want to find out if the tooth is sensitive to biting pressure or to cold or hot things. 
Sometimes teeth will develop an infection in the nerve, which can cause sensitivity. If this is the case, the infection can be removed from the tooth by getting a root canal, which is not as scary as it sounds! Another option is to remove the tooth. You can discuss these options with your dentist and see which one is best for you if that is what is happening with your tooth.