To reproduce:
1. Open the user's attached project
2. Open the "LWRP-Discard" scene found it Assets/LWRP
3. Take a look at the Quad's shadow
4. Set the SRP in Graphics Settings to "LWRP"
5. Open the Scene in Assets/BuiltIn and observe the Quad's shadow there

Expected result: The Shader has alpha clipping for opaque objects and clip/discard the shadow pass for clipped objects
Actual result: Alpha clipping does not work and the cast shadows are visible through the Quad on parts it has full opacity

Reproduced with LWRP versions 3.3.0, 3.1.0, 3.0.0, 2.0.8