Your photos are not stored in Lightroom, and the answer is that there is no known limit.
The are folk using Lr with in excess of 250,000 photos. My own catalog is just under 100,000. So, your 20,000 isn't going to be too many.
Hi Ian, thank you for your prompt reply. I am amazed that someone replied to my question.
I am most grateful that you took the time to help me.
Hi dj, thank you for your prompt reply. That means that I can use Lightroom with confidence. Elements 10, on my MAC slowed down when 15,000 pics were in the catalogue. At 20,000 it became un workable.