I forgot to address the drainage issue:
Mine grow in clay based soils, but I would not classify them as slow draining. Water never EVER just sits at the surface, either in the spring or after heavy rain. On the east side of my house, one plant's soil is invaded with maple roots that effectively suck up moisture. The other is on a gentle slope on the north side of the house.
In a warmer climate then me, your cold and wet period will be longer than mine because my soils are frozen in winter longer and deeper. Not a plus for plants that need good drainage in the winter. My guess, though, is that your plants will be fine. Unless you have a place with better drainage to move them to, I'd say leave them alone. Improving the soil just where the lilies are (and not the rest of the garden) will not help. Clay soil that is settled and uncultivated for more than 2 months holds less water than the same soil freshly dug. So any cultivating in the soil should be very light and at the surface only.
