I wouldn't hesitate to divide a blooming lily. It may stop blooming until it is re-established, but the plant will be fine.
As far as dividing a lily under 1 year old...technically, you might be able to, but if the pot isn't large enough to accommodate at least 1 year of growth the pot is too small. The smaller you keep a lily divided, the fewer flowers you'll get. I like to use pots large enough for at least 2 years of growth...3 is better. Anything bigger is nearly impossible to handle. By year 2 and 3, you'll have bunches of flowers all summer. When it gets to the point where you can't push the fertilizer tab into the pot, it is time to repot.