Combine softened butter and sugar and mix until light and fluffy, about 2 minutes.
Add flour and salt. Mix until combined.
Add lemon zest and lemon juice.
Wrap dough in plastic wrap and roll into a log.
Chill for at least 1 hour.
Slice into 1/2 rounds and bake at 325 for 9-11 minutes until just browned around the edges.
For the glaze, combine powdered sugar and lemon juice. Dip cookies into the glaze.