Two things about that (overanalyzing your shower thought):

1. Geneticists have what they call the "50/500 rule," which basically means that you need at least 50 people to avoid inbreeding, and at least 500 to avoid genetic drift. So while three people are 50% better than two, it's not going to come close to avoiding inbreeding.

2. If you read up on Lilith, including your Wikipedia link, you'll see her name only comes up once in the Bible, and it's not as Adam's wife. All the stuff about her comes from other things, including Babylonian and Mesopotamian writings, and lots of folklore from the middle ages. And at that, she's sometimes Adam's first wife, with different explanations about what happened to her that really in her not coming back to the garden, or she's a demon. So there's not much likelihood that she's contributing to the gene pool.