Haha, thanks... I think? Sounds like the midpoint of a horror movie ;)
Yes, you can currently impregnate Lily - that was added a few updates back. If you're getting the "Something is preventing..." message then either:
1. She's already pregnant (it takes about four days for the belly to show, and a week until birth)
2. She's not Love level 4
3. You already have a child of hers in the day care
Hope that helps! :)