When you say it "doesn't work", what exactly does happen? Do you end up on a different page? Do you get any error messages?
Is this a Linux (Apache) server? If it's Windows (IIS or Windows Server), .htaccess will be ignored. There's probably some other way to redirect, in that case. Worst case, you make index.html:
<html>Note that this will always go to the same place on your FB page (anything else the visitor types in will be discarded).
<title>Redirect to my Facebook page</title>
<meta http-equiv="refresh" content="0; URL=https:......" />
You should be immediately redirected to my Facebook page. If not, <a href="https:....">click here</a>.
Is your .htaccess file in the / directory (site root)? Is it readable (644 permissions)? Is there anything else in it?
Note that using $1 will tack on anything else the visitor added to your LP URL, which may or may not be valid on FB. You can drop the /$1 if you want them to go to the same URL each time.
P.S. If this is a brand-new LP account (and domain name), remember that it can take up to 72 hours (usually much less) for the Web's Domain Name Service to get updated around the world. If your LP domain isn't being recognized yet, try back in a day.