When you apply sharpening in Lightroom's Develop module and open the image in the Library module, it looks as though the sharpening isn't applied.
View the image at 1:1 or 100% view.
Some of the effects applied in Develop are too intensive and detailed for them to appear in thumbnail images or in reduced views. To see the affects as they are applied, view the image in 1:1 view or larger in Develop and in Library. If you're viewing them in Photoshop, use 100% view.
To see more a more accurate rendering of the sharpen effect in the Library module, even in thumbnails or reduced-size views, generate 1:1 previews when you import. To generate 1:1 previews, choose Library > Previews > Build 1:1 Previews.