Spent lily bulbs.

I agree - L. regale is usually a very straightforward lily and lasts for a very long time. I used to have it in a previous garden, and I was there for a considerable time - over fifteen years.
I've never tried any lilies from seed, but as well as growing on the scales, you can also grow them from the little bulbils [between leaf stems and main stem] although it would be too late for that.
It sounds like they might just be congested in the pots though. I check mine every few years and remove one or two if there's too much root in them, which is usually the case.

I wouldn't expect GCs to have lilies at this time of year - late winter/early spring is the time for them. Same with online suppliers - if they're good ones, although you can sometimes pre order at the start of the year.

 

I will try to remember you noisette 47 next time I am having a clear out. I think I might try burying the small bulbs under the new ones to grow on. Not something I have ever tried before.