Ooooh my ... just let me hug the life out of you, my dear anon, be so kind. This is absolutely delightful! ^^

You stroke the right notes with many things I personally love - ghost stories, cats (that really made me smile), interesting and not-quite explained mystery, Holmes being Holmes, brave Watson and competent Lestrade.
I truly adore Lestrade in here. And those most interesting powers he hides. ^^ You managed to create pleasant, slightly spooky atmosphere.
Also, the UST was lovely – not too much, certainly not obtrusive, and definitely welcomed.

And this sentence: Lestrade glared at him, but wisely refrained from getting provoked into a verbal competition he had no hope of winning. The mental picture it provided is most lovely.

Many thanks to you!