I know this seems like a really disgusting problem and it really has no solutions except for one.
Lily likes the toilet. I mean *really* likes the toilet. Every time she hears the door open she races to the bathroom so that she can stick her hand in the toilet. Yesterday I didn't catch her in time and when I caught up with her she was playing in the toilet water WHILE Rachel was peeing into the toilet. I have to wash Lily's hands at least half a dozen times a day. The two older girls have learned to KEEP THE DOOR CLOSED AT ALL TIMES but Rachel is still a bit dense about this. She just leaves the door open for Lily to come play. The other girls all had a mild interest in the toilet but I've never seen it this bad. AARRGGHHHHH!