If it's your first time meeting her, don't invite her into your home.
Unless she is an established provider with good reviews and you feel that you can trust her.
But since you said you're scared of LE, sounds like a random backpage girl.

As far as the neighbors situation, have her park in your driveway.
That's what a few veterans suggested.
Some providers even ask you to park in their driveway when you go to their location to avoid neighbors getting suspicious.

They might also leave the door open 5-10 minutes before the scheduled appointment time so that you can just walk in instead of knocking in case there are spectators.

If you select a well reviewed provider who does outcalls, you should be fine.  

You shouldn't have to worry about the neighbors if you occasionally have a friend or relative visit your home and they dont think twice about them - so they shouldn't think twice about another friend coming by to visit you.  (just dont ask her to dress in some eye catching manner that would make her look obviously like she's a hooker).

Say she isn't what she looks like...how can you end the session gracefully without her freaking out and making a scene?

You gotta be super careful if you have an outcall.

but agree not on the first date.  Way too many things that can happen.   If it doesn't work out OR if you decide you don't want to see her again...  she doesn't know where you live.