I'd opine that you don't need "optimal" settings but rather just "more than adequate to meet the capability offered". You ask with reference to Lightroom, and I'm commenting mentioning Irfanview, but the core requirements will be much the same.
A Facebook "high quality' photo page is typically about 3 megapixel. Actual dimensions vary slightly.
A quick looks shows 2048 x 1366, 2048 x 1365,... . I typically load from a 3:2 image so I'm not sure what makes FB change size slightly. Downloading a Facebook high resolution image typically gives around 300 kB file size. You could upload at a similar size but risk them resizing with no "headroom"*.
Facebook claim that if you upload a photo at 2048 pixels wide that they do no resize it. This may be true, but they may downgrade the quality.
I just uploaded a 2048 x 1365, 538.97 kB image. I then downloaded it and compared the two. The downloaded files was also 2048 x 1365 but file size was 246.72 kB. THey do strip off EXIF data, but a flicker comparison of the two shows that they also strip off quality. Results were "reasonable" but fine detail was noticeably worse in many areas. Not so much that you would probably notice with two prints side by side. Pixel peeping / flicker comparator was really required - but obvious enough once done. Whether uploading with higher resolution/ more detail will help is tbd.
Short:
JPEG 90 quality more than adequate
3000 x 2000 resolution is downsized by FB to about 2048 x xxxx
6000 x 4000 works but adds nothing.
Files size of 1 to 2 MB works well.
When posting for populist viewing I may selectively somewhat over-saturate or slightly over sharpen compared to increase image impact at expense of best 'similitude'. Varies by photo.
The following may be seen as hijacking this question to my own ends.
BUT the best way of seeing if my answer suits is to see what I think works for me and you can decide if that suits you. And, I'd be interested in what others think in turn. The normal viewers of these photos like them BUT the audience here is a somewhat different one.
Most of My Facebook Wall Photos here were uploaded with the above settings.
They seem to exceed the capabilities of a "Full HD" monitor when viewed full screen on Facebook.
I'd be interested in (polite) comment on the perceived adequacy of those photos for the purpose of FB display. That's my "Wall Photos" page where I post photos of mine that catch my fancy along the way. Some are limited by cropping (sparrows, dove, flying dog, birds nest, ...) or marginal conditions (lying on railway track at night, 35 year old off-print photo of my wife, ...) but most are restricted by the FB format.
My aim is to provide photos of mine that I like that are likely to be of interest to others. Seems to work :-). In this role saturation may be set higher than it may otherwise be. Sharpening may sometimes be slightly sharper than would otherwise be.
If you want to get every little bit out of what FB can display you MAY get success trying to upload an image that fits their end size exactly, but I've decided that an image in the 1MB - 2MB range after JPEG 90 saving from Irfanview provides result that is close enough to the original that nobody is going to complain when viewed at "full HD" resolution. Full HD is slightly lower res than FB provides so a monitor which refits your image to a full HD screen is going to be reasonably well served by an uploaded image in the 1-2 MB range.
My source images re usually 6000 x 4000 (Sony A77) or ~ 4000 x 3000 (Nikon D700). Some are from years gone by with cameras of lower resolutions. (Lowest probably 2003 Minolta 7Hi 5Mp). I usually use Irfanview for quick process and post. A save at JPG 90 setting produces a result that is pixel-peeping level essentially identical to a JPG source and will cvom,press a camera JPG by about 2 to 6 times (depending on camera settings). I have more upload bandwidth than needed so speed of upload (about 1 mbps - varies) and FB willingness to accept files are the main constraints. If a files is over say 2 MB I may resize x 50% X & Y to 1/4 original size on A77. Maybe 70% x 70% on D700. FB will accept larger files but large uploads seem to fail more often for unspecified reasons.
- "Headroom" - If you could get FB to accept files of a size that matches theirs then you could upload files around 300 kB in many cases. However, even if you exactly match their displayed size there is no guarantee that they will not "play" with the image size and every chance that they will. If you upload at comfortably above their displayed resolution you give their downsizing algorithm something to deal with intelligently.
It MAY be that uploading at say 4096 x xxx will allow their 2048 x yyy image to be produced with best results. But, their is no guarantee of this. I find that 3000 x 2000 usually produces displayed FB images that are acceptable for the usual uses and not greatly different from what would be obtained by downsizing to 2048 x xxx yourself.