Jeanr:

Fall and early spring are good times to divide lilies--after they have gone dormant or before they start sending shoots. Now that the shoots are showing, just fertilize them, and enjoy the flowers!

One thing i"ve learned since I do like having them growing in clumps for a better display , is that allowing them to multiply for a few years does no harm and you'll still get the extra bulbs. I guess however, after a point, they do start to crowd each other and then it may be necessary to thin them out a bit. If it's a new bulb , and not overly crowded by neighboring plants, I'd leave it alone, unless you wish to plant some elsewhere from the new ones you get.
After some reluctance by one oriental bulb in one location I moved it to another spot , where it seemed much happier and it subsequently produced about ten new bulbs before I did have to thin out the clump. A very nice show indeed that was, with up to fifty flowers open at a time! A bit overpowering smell wise however!!