Yeah you definately do not want to rush things, if you are going to adopt from a shelter or a private adoption such as craigslist, bring Lily with to see how the dog does before bringing the dog home which would be my advice to you.

About the cats, take it VERY, VERY slow with them. Cats are very different and not all of them care for dogs. My boys love the dogs but Angel can do without them.

Maybe try going with a dog Lily's size or not much bigger than her? She could just have been intimidated by Duke's size. Do you have any idea what breed or in the mix range you are looking for? Maybe get a mellow adult lab from a shelter or something?