Not a problem. Nothing is deleted when the trial expires.
Just to add to DJ's answer, your images are never in Lightroom - they're simply referenced in Lightroom's database/catalogue.
So nothing that might happen to Lr will have the kind of impact on your images that you're worried about.
You don't have to do anything except type your Registration Number in your trial version when you purchase. ALL you settings and photo adjustment will be there. There is no difference between the trial and purchased version. DO NOT remove Lightroom and reinstall, just imput your registration number and all will be the same.