Export without losing quality

Something you always want to consider is the use of the images. For example, are you planning on printing the files and if so, how large, are they for social media, is a client using them in a publication...?

The highest quality will always be the original full resolution, and whenever we reduce files for a specific output, we lose quality.

Your best bet is to always work on the raw file and then export/output for the specific need.

I don't think using Photoshop will make any difference, Lightroom is very capable when it comes to resizing files on export.

But as others have said, a 1080 pixel file is what it is, you only have so many pixels, and you cannot expect the quality to be the same as for the full resolution file.

Having said that, it's perfectly possible to export a 1080 pixel file that looks good.

It helps a lot to have a sharp, good quality original that has been properly processed.

I see that you are using Output sharpening set to High, which in my experience leads to over sharpening for a normally sharp image. I find that Standard sharpening works well in most cases.

And for the record, using Long edge for image sizing is perfectly OK, it does not stretch the image.

An image that is reduced to just 1080 pixels on the long side is a significant reduction in size in today's image size. For instance, my camera isn't very recent. However, a full-sized image has 6000 pixels on the long side. So exporting an image with just 1080 pixels is really reducing the size, and therefore is going to degrade the quality of the image. If you want the best quality you should consider not reducing the size. If you must reduce the size to meet the requirements of some website or some project you are doing then you might consider creating the smaller image using Photoshop to see if that makes a difference.

Well, In theory it won't look as good as the original when you create a JPEG, because you are compressing the image.

That said, I am not sure what resolution your original image is, but if you're resizing down to 1080px on the long edge, you very well could be bringing the resolution down quite a bit. Try unchecking "Resize to Fit" to keep the original source resolution.

95% is certainly a fine quality setting for JPEG, but again if you're taking a much higher resolution source image, then bringing it down to 1080px wide, and stretching that to fill your frame, it won't be as sharp as the full resolution copy, which very likely is supersampling down to your display.