How do you purge your searches so that when you type in a letter, a previous search doesn't show up under it?

That's in regards to one of your LW preferences settings, namely Autocompletion of text fields. In order to turn this off, go to LW's menu Tools-Options & View. Select Autocomplete & untick the box for enable.
I was just thinking, originally I had mine set to off & didn't learn about it until I hit this forum. Now that I've used it & learnt a few tricks about how to use it (such as searching material by the same artist), it saves me from continually pasting the search criteria in, which is what I used to do. Mind you, just a few mths ago I was still using LW2 & I couldn't even paste into the search. I found that very annoying. So I guess it's however it suits the particular person.