Once you import into Lightroom you're going to want to do
all of your file management for those images in Lightroom. Previews are saved in the LR catalog, so if you delete or move the images using other means then they'll still appear in LR with an '!' in the corner stating that the corresponding file is not available. A nice thing about that is, if you use Smart Previews, you'll still be able to produce fairly good sized, shareable JPG's from the preview if the deletion was accidental.
That said, I'm a little perplexed by your issue, particularly what you mean by
I have named a batch of RAW images in My Pictures. It sounds like you're importing first to your computer and then to Lightroom from there. If that's the case, I highly recommend using the LR Import facility to pull them in straight from the camera to avoid stuff like this. I don't know why
deleted images are still showing up, but one guess would be that they're not actually deleted but in the Trash and LR is finding them for some reason?