I did extended nursing with my son, and I've had mamograms during breastfeeding. At that time, it was extremely difficult to find a lab that would DO the mamogram on me. They said they wanted to wait until I was done. The problem was, they found spots they were concerned about on the last mamo I had, just before I got pregnant. So my OB insisted that I have a mamo right away, and he called around to find a lab that would agree. They just weren't very familiar with breastfeeding at that time.
I checked at the time with LLL, and they said it was okay to have it, but I did pump for a while afterwards and dispose of the milk. I had a stockpile of pumped milk to work from in the freezer, during that time.
I've had to have regular mamograms since my late 20s. My sister had lumps, and my aunt had breast cancer, so I was considered high risk. They wanted one baseline mamo, and regular ones after that to keep things monitored. I also have dense tissue, and it has caused concern before, but the follow up mamo alleviated the concerns.
I'd recommend contacting the La Leche League. I would expect them to have the most current and up to date info on mamograms and breastfeeding, and what precautions to take.
Good luck!